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https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply hcost.cost_ale.le_bound
case h₀ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: case h₀ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
exact (hcost.toComputable.has_result _).elim λ _ h ↦ ⟨(_, _), h⟩
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply splitTimeCost hf (TracedProgram.sound'_subroutine_next h)
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₁.a α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.mem_bind_of_mem hm
case h₁.a α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs ins...
case h₁.a α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.a α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.mem_map_of_mem
case h₁.a α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs ins...
case h₁.a.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs i...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.a α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.get_mem
case h₁.a.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs i...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.a.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFu...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_le_of_eq _
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Nat.add_assoc
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add _
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (le_of_eq (Eq.symm (Complexity.CostFunction.flatMap_some hm _)))
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_eq_of_le
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Eq.trans
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₁.h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs in...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_comm
case h₁.h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs in...
case h₁.h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs in...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFun...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (Nat.add_assoc _ _ _).symm
case h₁.h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs in...
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFun...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add _ (le_refl _)
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_eq_of_le
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (Nat.add_assoc _ _ _).symm
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add _ (le_refl _)
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_eq_of_le
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_comm
case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add (le_refl _)
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_le_of_eq _
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Eq.symm
case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝...
case h₂.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Complexity.CostFunction.flatMap_some
case h₂.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs ins...
case h₂.h.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs i...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.mem_bind_of_mem
case h₂.h.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs i...
case h₂.h.h.ha α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model f...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFu...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply hm
case h₂.h.h.ha α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model f...
case h₂.h.h.hf α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model f...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h.ha α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.Cos...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.get_mem
case h₂.h.h.hf α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model f...
case h₂.h.h.hf.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h.hf α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.Cos...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (h.left _ _ hm).elim λ hsome _ ↦ hsome
case h₂.h.h.hf.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model...
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h.hf.h α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.C...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_refl
α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝³ : Complexity.Computable Encoding.Model fs inst✝² : Comp...
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁷ : Complexity.Coding α Memory β : Type u_2 inst✝⁶ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁵ : Complexity.Coding γ Memory inst✝⁴ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Stack.hasTimeCost_recurse_le _
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
case hr α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
rw [TracedProgram.sound_recurse_arg (TracedProgram.sound_of_sound' h _ _ hm)]
case hr α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case hr α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case hr α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Program.hasResult_of_sound hf
case hr α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₀ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case hr α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
rw [TracedProgram.sound_recurse_arg (TracedProgram.sound_of_sound' h _ _ hm)]
case h₀ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₀ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₀ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Stack.timeCost_sound
case h₀ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₀.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₀ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Program.halts_of_sound hf
case h₀.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₀.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply splitTimeCost hf (TracedProgram.sound'_recurse_next h)
case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₁.a α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.mem_bind_of_mem hm
case h₁.a α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
case h₁.a α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.a α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.mem_map_of_mem
case h₁.a α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
case h₁.a.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs i...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.a α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.get_mem
case h₁.a.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs i...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.a.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFu...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_le_of_eq _
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Nat.add_assoc
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add _
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (le_of_eq (Eq.symm (Complexity.CostFunction.flatMap_some hm _)))
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_eq_of_le
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Eq.trans
case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₁.h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_comm
case h₁.h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
case h₁.h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFun...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (Nat.add_assoc _ _ _).symm
case h₁.h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFun...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add _ (le_refl _)
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_eq_of_le
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Eq.trans
case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₁.h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
Please generate a tactic in lean4 to solve the state. STATE: case h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_comm
case h₁.h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
case h₁.h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.h₁ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFun...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Nat.add_assoc _ _ _
case h₁.h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs in...
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₁.h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFun...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add (le_refl _)
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply add_le_add (le_refl _)
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_of_le_of_eq _
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Eq.symm
case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝...
case h₂.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
Please generate a tactic in lean4 to solve the state. STATE: case h₂ α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFuncti...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Complexity.CostFunction.flatMap_some
case h₂.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs ins...
case h₂.h.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs i...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.mem_bind_of_mem
case h₂.h.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs i...
case h₂.h.h.ha α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model f...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFu...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply hm
case h₂.h.h.ha α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model f...
case h₂.h.h.hf α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model f...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h.ha α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.Cos...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply Option.get_mem
case h₂.h.h.hf α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model f...
case h₂.h.h.hf.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h.hf α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.Cos...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply (h.left _ _ hm).elim λ hsome _ ↦ hsome
case h₂.h.h.hf.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model...
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
Please generate a tactic in lean4 to solve the state. STATE: case h₂.h.h.hf.h α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.C...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Trace.CostedProgram.splitTimeCost
[244, 1]
[349, 16]
apply le_refl
α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝¹ : Complexity.Computable Encoding.Model fs inst✝ : Compl...
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝⁵ : Complexity.Coding α Memory β : Type u_2 inst✝⁴ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝³ : Complexity.Coding γ Memory inst✝² : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ i...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Program.splitTimeCost
[433, 1]
[438, 18]
intro a
TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Computable ...
TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Computable ...
Please generate a tactic in lean4 to solve the state. STATE: TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs ...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Program.splitTimeCost
[433, 1]
[438, 18]
apply le_trans
TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Computable ...
case a TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Comp...
Please generate a tactic in lean4 to solve the state. STATE: TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs ...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Program.splitTimeCost
[433, 1]
[438, 18]
exact (Stack.timeCost_le_iff _ (Program.halts_of_sound h _)).mp (p.costedMatches ▸ p.costed.splitTimeCost (costed_sound h) (costed_sound' h) a _ (Option.mem_some_iff.mpr rfl))
case a TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Comp...
case a TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Comp...
Please generate a tactic in lean4 to solve the state. STATE: case a TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ ...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Trace/Cost.lean
HMem.Program.splitTimeCost
[433, 1]
[438, 18]
exact le_refl _
case a TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ → δ cs : Complexity.CostFunction γ ℕ inst✝² : Complexity.Comp...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a TracedProgram : Sort ?u.211566 α : Type u_1 inst✝⁶ : Complexity.Coding α Memory β : Type u_2 inst✝⁵ : Complexity.Encoding β Memory f : α → β tp : TracedProgram γ δ : Type inst✝⁴ : Complexity.Coding γ Memory inst✝³ : Complexity.Encoding δ Memory fs : γ ...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_sum_getm_t
[73, 9]
[74, 59]
cases v <;> simp
α : Type u_1 β : Type u_2 inst✝¹ : Encoding α Memory inst✝ : Encoding β Memory v : α ⊕ β ⊢ Memory.getm (encode v) true = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 β : Type u_2 inst✝¹ : Encoding α Memory inst✝ : Encoding β Memory v : α ⊕ β ⊢ Memory.getm (encode v) true = 0 TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeList_inj
[88, 1]
[92, 90]
simp[encodeList]
α : Type u_1 inst✝ : Encoding α Memory head✝ : α tail✝ : List α ⊢ encodeList [] = encodeList (head✝ :: tail✝) → [] = head✝ :: tail✝
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory head✝ : α tail✝ : List α ⊢ encodeList [] = encodeList (head✝ :: tail✝) → [] = head✝ :: tail✝ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeList_inj
[88, 1]
[92, 90]
simp[encodeList]
α : Type u_1 inst✝ : Encoding α Memory head✝ : α tail✝ : List α ⊢ encodeList (head✝ :: tail✝) = encodeList [] → head✝ :: tail✝ = []
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory head✝ : α tail✝ : List α ⊢ encodeList (head✝ :: tail✝) = encodeList [] → head✝ :: tail✝ = [] TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeList_inj
[88, 1]
[92, 90]
simp[encodeList, Iff.intro (encodeList_inj lhs rhs) λ h ↦ h ▸ rfl]
α : Type u_1 inst✝ : Encoding α Memory head✝¹ : α lhs : List α head✝ : α rhs : List α ⊢ encodeList (head✝¹ :: lhs) = encodeList (head✝ :: rhs) → head✝¹ :: lhs = head✝ :: rhs
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory head✝¹ : α lhs : List α head✝ : α rhs : List α ⊢ encodeList (head✝¹ :: lhs) = encodeList (head✝ :: rhs) → head✝¹ :: lhs = head✝ :: rhs TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.rawDecodeList_inv
[101, 1]
[103, 87]
simpa [encodeList, decodeList, rawDecodeList] using rawDecodeList_inv tl
α : Type u_1 inst✝ : Coding α Memory head✝ : α tl : List α ⊢ decodeList (encodeList (head✝ :: tl)) = some (head✝ :: tl)
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory head✝ : α tl : List α ⊢ decodeList (encodeList (head✝ :: tl)) = some (head✝ :: tl) TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.tupleInj_eq
[145, 9]
[147, 44]
simp [encodeFinTuple_def, List.ofFn_inj']
α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : Fin N₀ → α f₁ : Fin N₁ → α ⊢ (encode f₀ = encode f₁) = (N₀ = N₁ ∧ HEq f₀ f₁)
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : Fin N₀ → α f₁ : Fin N₁ → α ⊢ (encode f₀ = encode f₁) = (N₀ = N₁ ∧ HEq f₀ f₁) TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_inj
[168, 1]
[180, 41]
simpa [encodeOp] using λ h ↦ funext λ x ↦ Subsingleton.elim _ x ▸ h
α : Type u_1 inst✝ : Encoding α Memory f₀ f₁ : (Fin 0 → Bool) → α ⊢ encodeOp f₀ = encodeOp f₁ → f₀ = f₁
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory f₀ f₁ : (Fin 0 → Bool) → α ⊢ encodeOp f₀ = encodeOp f₁ → f₀ = f₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_inj
[168, 1]
[180, 41]
simpa [encodeOp, λ b ↦ Iff.intro (encodeOp_inj (f₀ ∘ (Fin.cons (α := λ _ ↦ Bool) b)) (f₁ ∘ (Fin.cons (α := λ _ ↦ Bool) b))) (λ h ↦ h ▸ rfl)] using λ hf ht ↦ funext λ y ↦ Fin.cons_self_tail y ▸ match y 0 with | false => congrFun hf (Fin.tail y) | true => congrFun ht (Fin.tail y)
α : Type u_1 inst✝ : Encoding α Memory N : ℕ f₀ f₁ : (Fin (N + 1) → Bool) → α ⊢ encodeOp f₀ = encodeOp f₁ → f₀ = f₁
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N : ℕ f₀ f₁ : (Fin (N + 1) → Bool) → α ⊢ encodeOp f₀ = encodeOp f₁ → f₀ = f₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
simpa [decodeOp, encodeOp] using funext λ _ ↦ congrArg _ (funext finZeroElim)
α : Type u_1 inst✝ : Coding α Memory x✝ : (Fin 0 → Bool) → α ⊢ decodeOp (encodeOp x✝) = some x✝
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory x✝ : (Fin 0 → Bool) → α ⊢ decodeOp (encodeOp x✝) = some x✝ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
simp [decodeOp, encodeOp, decodeOp_inv (N := N)]
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ decodeOp (encodeOp g) = some g
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ (fun g_1 => match g_1 0 with | false => g (Fin.cons false (Fin.tail g_1)) | true => g (Fin.cons true (Fin.tail g_1))) = g
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ decodeOp (encodeOp g) = some g TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
apply funext
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ (fun g_1 => match g_1 0 with | false => g (Fin.cons false (Fin.tail g_1)) | true => g (Fin.cons true (Fin.tail g_1))) = g
case h α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ ∀ (x : Fin (N + 1) → Bool), (match x 0 with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ (fun g_1 => match g_1 0 with | false => g (Fin.cons false (Fin.tail g_1)) | true => g (Fin.cons true (Fin.tail g_1))) = g TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
intro x
case h α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ ∀ (x : Fin (N + 1) → Bool), (match x 0 with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x
case h α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool ⊢ (match x 0 with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x
Please generate a tactic in lean4 to solve the state. STATE: case h α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α ⊢ ∀ (x : Fin (N + 1) → Bool), (match x 0 with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
match h:x 0 with | true => apply congrArg g exact h ▸ Fin.cons_self_tail _ | false => apply congrArg g exact h ▸ Fin.cons_self_tail _
case h α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool ⊢ (match x 0 with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool ⊢ (match x 0 with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
apply congrArg g
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = true ⊢ (match true with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = true ⊢ Fin.cons true (Fin.tail x) = x
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = true ⊢ (match true with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
exact h ▸ Fin.cons_self_tail _
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = true ⊢ Fin.cons true (Fin.tail x) = x
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = true ⊢ Fin.cons true (Fin.tail x) = x TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
apply congrArg g
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = false ⊢ (match false with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = false ⊢ Fin.cons false (Fin.tail x) = x
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = false ⊢ (match false with | false => g (Fin.cons false (Fin.tail x)) | true => g (Fin.cons true (Fin.tail x))) = g x TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.decodeOp_inv
[195, 1]
[209, 35]
exact h ▸ Fin.cons_self_tail _
α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = false ⊢ Fin.cons false (Fin.tail x) = x
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Coding α Memory N : ℕ g : (Fin (N + 1) → Bool) → α x : Fin (N + 1) → Bool h : x 0 = false ⊢ Fin.cons false (Fin.tail x) = x TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injN
[221, 1]
[226, 53]
cases N₁ <;> simp [encodeOp_zeroDef, encodeOp_succDef]
α : Type u_1 inst✝ : Encoding α Memory N₁ : ℕ x✝¹ : (Fin 0 → Bool) → α x✝ : (Fin N₁ → Bool) → α ⊢ encode x✝¹ = encode x✝ → 0 = N₁
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N₁ : ℕ x✝¹ : (Fin 0 → Bool) → α x✝ : (Fin N₁ → Bool) → α ⊢ encode x✝¹ = encode x✝ → 0 = N₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injN
[221, 1]
[226, 53]
simp [encodeOp_zeroDef, encodeOp_succDef]
α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ x✝¹ : (Fin (N₀ + 1) → Bool) → α x✝ : (Fin 0 → Bool) → α ⊢ encode x✝¹ = encode x✝ → N₀ + 1 = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ x✝¹ : (Fin (N₀ + 1) → Bool) → α x✝ : (Fin 0 → Bool) → α ⊢ encode x✝¹ = encode x✝ → N₀ + 1 = 0 TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injN
[221, 1]
[226, 53]
simpa [encodeOp_succDef] using λ _ ↦ encodeOp_injN
α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : (Fin (N₀ + 1) → Bool) → α f₁ : (Fin (N₁ + 1) → Bool) → α ⊢ encode f₀ = encode f₁ → N₀ + 1 = N₁ + 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : (Fin (N₀ + 1) → Bool) → α f₁ : (Fin (N₁ + 1) → Bool) → α ⊢ encode f₀ = encode f₁ → N₀ + 1 = N₁ + 1 TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injEq
[228, 9]
[232, 48]
cases (encodeOp_injN h)
α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : (Fin N₀ → Bool) → α f₁ : (Fin N₁ → Bool) → α h : encode f₀ = encode f₁ ⊢ N₀ = N₁ ∧ HEq f₀ f₁
case refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ f₁ : (Fin N₀ → Bool) → α h : encode f₀ = encode f₁ ⊢ N₀ = N₀ ∧ HEq f₀ f₁
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : (Fin N₀ → Bool) → α f₁ : (Fin N₁ → Bool) → α h : encode f₀ = encode f₁ ⊢ N₀ = N₁ ∧ HEq f₀ f₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injEq
[228, 9]
[232, 48]
simp [h, ← encodeInjEq]
case refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ f₁ : (Fin N₀ → Bool) → α h : encode f₀ = encode f₁ ⊢ N₀ = N₀ ∧ HEq f₀ f₁
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ f₁ : (Fin N₀ → Bool) → α h : encode f₀ = encode f₁ ⊢ N₀ = N₀ ∧ HEq f₀ f₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injEq
[228, 9]
[232, 48]
cases h.left
α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : (Fin N₀ → Bool) → α f₁ : (Fin N₁ → Bool) → α h : N₀ = N₁ ∧ HEq f₀ f₁ ⊢ encode f₀ = encode f₁
case refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ f₁ : (Fin N₀ → Bool) → α h : N₀ = N₀ ∧ HEq f₀ f₁ ⊢ encode f₀ = encode f₁
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : Encoding α Memory N₀ N₁ : ℕ f₀ : (Fin N₀ → Bool) → α f₁ : (Fin N₁ → Bool) → α h : N₀ = N₁ ∧ HEq f₀ f₁ ⊢ encode f₀ = encode f₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injEq
[228, 9]
[232, 48]
cases h.right
case refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ f₁ : (Fin N₀ → Bool) → α h : N₀ = N₀ ∧ HEq f₀ f₁ ⊢ encode f₀ = encode f₁
case refl.refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ : (Fin N₀ → Bool) → α h : N₀ = N₀ ∧ HEq f₀ f₀ ⊢ encode f₀ = encode f₀
Please generate a tactic in lean4 to solve the state. STATE: case refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ f₁ : (Fin N₀ → Bool) → α h : N₀ = N₀ ∧ HEq f₀ f₁ ⊢ encode f₀ = encode f₁ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encodeOp_injEq
[228, 9]
[232, 48]
rfl
case refl.refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ : (Fin N₀ → Bool) → α h : N₀ = N₀ ∧ HEq f₀ f₀ ⊢ encode f₀ = encode f₀
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refl.refl α : Type u_1 inst✝ : Encoding α Memory N₀ : ℕ f₀ : (Fin N₀ → Bool) → α h : N₀ = N₀ ∧ HEq f₀ f₀ ⊢ encode f₀ = encode f₀ TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
refine Nat.binaryRec' (n := n) Memory.zero_def'.symm ?hi
n : ℕ ⊢ encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2))
case hi n : ℕ ⊢ ∀ (b : Bool) (n : ℕ), (n = 0 → b = true) → encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) → encode (Nat.bit b n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Nat.bit b n / 2))
Please generate a tactic in lean4 to solve the state. STATE: n : ℕ ⊢ encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) TACTIC:
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
intro b n hn _
case hi n : ℕ ⊢ ∀ (b : Bool) (n : ℕ), (n = 0 → b = true) → encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) → encode (Nat.bit b n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Nat.bit b n / 2))
case hi n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (Nat.bit b n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Nat.bit b n / 2))
Please generate a tactic in lean4 to solve the state. STATE: case hi n : ℕ ⊢ ∀ (b : Bool) (n : ℕ), (n = 0 → b = true) → encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) → encode (Nat.bit b n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit ...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
apply Eq.trans
case hi n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (Nat.bit b n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Nat.bit b n / 2))
case hi.h₁ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (Nat.bit b n) = ?hi.b case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)...
Please generate a tactic in lean4 to solve the state. STATE: case hi n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (Nat.bit b n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Na...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
apply congrArg (encode (α := List Bool))
case hi.h₁ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (Nat.bit b n) = ?hi.b case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)...
case hi.h₁ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ Nat.bits (Nat.bit b n) = ?m.80295 n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ Li...
Please generate a tactic in lean4 to solve the state. STATE: case hi.h₁ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (Nat.bit b n) = ?hi.b case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
apply Nat.bits_append_bit _ _ hn
case hi.h₁ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ Nat.bits (Nat.bit b n) = ?m.80295 n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ Li...
case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (b :: Nat.bits n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Nat.bit b n / 2))
Please generate a tactic in lean4 to solve the state. STATE: case hi.h₁ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ Nat.bits (Nat.bit b n) = ?m.80295 n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
apply Memory.mk_inj_iff.mpr
case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (b :: Nat.bits n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (encode (Nat.bit b n / 2))
case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ true = decide (Nat.bit b n ≠ 0) ∧ encode b = encode (decide (Nat.bit b n % 2 = 1)) ∧ encodeList (Nat.bits n) = encode (Nat.bit b n / 2)
Please generate a tactic in lean4 to solve the state. STATE: case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode (b :: Nat.bits n) = Memory.mk (decide (Nat.bit b n ≠ 0)) (encode (decide (Nat.bit b n % 2 = 1))) (enc...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
apply And.intro
case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ true = decide (Nat.bit b n ≠ 0) ∧ encode b = encode (decide (Nat.bit b n % 2 = 1)) ∧ encodeList (Nat.bits n) = encode (Nat.bit b n / 2)
case hi.h₂.left n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ true = decide (Nat.bit b n ≠ 0) case hi.h₂.right n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (...
Please generate a tactic in lean4 to solve the state. STATE: case hi.h₂ n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ true = decide (Nat.bit b n ≠ 0) ∧ encode b = encode (decide (Nat.bit b n % 2 = 1)) ∧ encodeList (Nat.bits n)...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
exact Eq.symm (decide_eq_true λ h ↦ absurd ((Nat.bit_eq_zero.mp h).right.symm.trans (hn (Nat.bit_eq_zero.mp h).left)) Bool.noConfusion)
case hi.h₂.left n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ true = decide (Nat.bit b n ≠ 0) case hi.h₂.right n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (...
case hi.h₂.right n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode b = encode (decide (Nat.bit b n % 2 = 1)) ∧ encodeList (Nat.bits n) = encode (Nat.bit b n / 2)
Please generate a tactic in lean4 to solve the state. STATE: case hi.h₂.left n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ true = decide (Nat.bit b n ≠ 0) case hi.h₂.right n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n...
https://github.com/calcu16/lean_complexity.git
d267eb4f3952c654f130a119311692c1c1a7cd71
HMem/Encoding/Basic.lean
HMem.Encoding.encode_nat_def
[244, 1]
[255, 6]
cases b <;> simp [-Nat.bit_false, -Nat.bit_true, Nat.bit_mod_two, Nat.bit_div_2]
case hi.h₂.right n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode b = encode (decide (Nat.bit b n % 2 = 1)) ∧ encodeList (Nat.bits n) = encode (Nat.bit b n / 2)
case hi.h₂.right.false n✝ n : ℕ a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) hn : n = 0 → false = true ⊢ encodeList (Nat.bits n) = encode n case hi.h₂.right.true n✝ n : ℕ a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) hn : n = 0 → ...
Please generate a tactic in lean4 to solve the state. STATE: case hi.h₂.right n✝ : ℕ b : Bool n : ℕ hn : n = 0 → b = true a✝ : encode n = Memory.mk (decide (n ≠ 0)) (encode (decide (n % 2 = 1))) (encode (n / 2)) ⊢ encode b = encode (decide (Nat.bit b n % 2 = 1)) ∧ encodeList (Nat.bits n) = encode (Nat.bit b n / 2) TACT...