| import Mathlib | |
| import OAI.Computability.MinUncut.Machines.MachineBinaryFormula | |
| namespace OAI | |
| section | |
| noncomputable section | |
| namespace MinUncut | |
| open MinUncutGames.BinaryEncoding | |
| lemma bitName_length_le (n : ℕ) : (nameBits n).length≤2*n+1 := by | |
| rw [nameBits_length] | |
| exact Nat.add_le_add_right (Nat.mul_le_mul_left _ (Nat.size_le.mpr n.lt_two_pow_self)) _ | |
| lemma Output.bits_length (G : Output) : | |
| G.bits.length=(nameBits G.vertices).length+G.vertices^2+(nameBits G.threshold).length := by | |
| unfold Output.bits | |
| simp only [List.length_append,List.length_flatMap,List.length_map,List.length_finRange] | |
| simp [pow_two] | |
| lemma Output.bits_length_le (G : Output) : | |
| G.bits.length≤2*G.vertices+1+G.vertices^2+(2*G.threshold+1) := by | |
| rw [G.bits_length] | |
| exact add_le_add (Nat.add_le_add_right (bitName_length_le _) _) (bitName_length_le _) | |
| end MinUncut | |
| end | |
| end | |
| end OAI | |