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720fa25 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part01
import OAI.GameTheory.SnakyConditional.Templates.Level06Part03
import OAI.GameTheory.SnakyConditional.Templates.Level06Part04
import OAI.GameTheory.SnakyConditional.Templates.Level06Part05
namespace OAI
namespace SnakyConditional
def required_132 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_132 : Finset Cell := ⟨(([(0, -2), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_132 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 0 (1, 2) required_89)]
def childrenD_132 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 0 (1, 2) envelope_89)]
theorem common_sub_132 : commonEnvelope childrenD_132 ⊆ insert (0, 0) required_132 := by decide
theorem child_required_sub_132 : ∀ j, childrenC_132 j ⊆ insert (0, 0) required_132 := by decide
theorem child_envelope_sub_132 : ∀ j, childrenD_132 j ⊆ envelope_132 := by decide
theorem pivot_mem_132 : (0, 0) ∈ envelope_132 := by decide
theorem children_work_132 : ∀ j, Template HasSnaky 4 (childrenC_132 j) (childrenD_132 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_89 0 (1, 2)).mono (by decide)
theorem row_works_132 : Template HasSnaky 5 required_132 envelope_132 := by
refine compose HasSnaky 4 childrenC_132 childrenD_132 children_work_132 (0, 0)
required_132 envelope_132 pivot_mem_132 child_required_sub_132 child_envelope_sub_132 ?_
intro b hb; exact common_sub_132 (mem_commonEnvelope childrenD_132 b hb)
def required_133 : Finset Cell := ⟨(([(-2, 0), (-1, -2), (0, -2), (0, -1), (0, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_133 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, -3), (-1, -2), (-1, 0), (0, -2), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (2, 1), (3, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_133 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -3) required_6), (placedSet 0 (1, 1) required_92)]
def childrenD_133 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -3) envelope_6), (placedSet 0 (1, 1) envelope_92)]
theorem common_sub_133 : commonEnvelope childrenD_133 ⊆ insert (0, 0) required_133 := by decide
theorem child_required_sub_133 : ∀ j, childrenC_133 j ⊆ insert (0, 0) required_133 := by decide
theorem child_envelope_sub_133 : ∀ j, childrenD_133 j ⊆ envelope_133 := by decide
theorem pivot_mem_133 : (0, 0) ∈ envelope_133 := by decide
theorem children_work_133 : ∀ j, Template HasSnaky 4 (childrenC_133 j) (childrenD_133 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 7 (-1, -3)).mono (by decide)
· exact (placed_template_map row_works_92 0 (1, 1)).mono (by decide)
theorem row_works_133 : Template HasSnaky 5 required_133 envelope_133 := by
refine compose HasSnaky 4 childrenC_133 childrenD_133 children_work_133 (0, 0)
required_133 envelope_133 pivot_mem_133 child_required_sub_133 child_envelope_sub_133 ?_
intro b hb; exact common_sub_133 (mem_commonEnvelope childrenD_133 b hb)
def required_134 : Finset Cell := ⟨(([(-1, -3), (-1, -1), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_134 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -4), (-1, -3), (-1, -1), (0, -3), (0, -2), (0, -1), (0, 0), (1, -1), (1, 0), (1, 1), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_134 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -4) required_6), (placedSet 0 (1, 0) required_82)]
def childrenD_134 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -4) envelope_6), (placedSet 0 (1, 0) envelope_82)]
theorem common_sub_134 : commonEnvelope childrenD_134 ⊆ insert (0, 0) required_134 := by decide
theorem child_required_sub_134 : ∀ j, childrenC_134 j ⊆ insert (0, 0) required_134 := by decide
theorem child_envelope_sub_134 : ∀ j, childrenD_134 j ⊆ envelope_134 := by decide
theorem pivot_mem_134 : (0, 0) ∈ envelope_134 := by decide
theorem children_work_134 : ∀ j, Template HasSnaky 4 (childrenC_134 j) (childrenD_134 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 7 (-1, -4)).mono (by decide)
· exact (placed_template_map row_works_82 0 (1, 0)).mono (by decide)
theorem row_works_134 : Template HasSnaky 5 required_134 envelope_134 := by
refine compose HasSnaky 4 childrenC_134 childrenD_134 children_work_134 (0, 0)
required_134 envelope_134 pivot_mem_134 child_required_sub_134 child_envelope_sub_134 ?_
intro b hb; exact common_sub_134 (mem_commonEnvelope childrenD_134 b hb)
def required_135 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-3, 1), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_135 : Finset Cell := ⟨(([(-6, 0), (-5, 0), (-4, 0), (-3, 0), (-3, 1), (-2, 0), (-2, 1), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_135 : Fin 3 → Finset Cell := ![(placedSet 0 (0, 1) required_7), (placedSet 4 (-2, 1) required_75), (placedSet 0 (1, 0) required_44)]
def childrenD_135 : Fin 3 → Finset Cell := ![(placedSet 0 (0, 1) envelope_7), (placedSet 4 (-2, 1) envelope_75), (placedSet 0 (1, 0) envelope_44)]
theorem common_sub_135 : commonEnvelope childrenD_135 ⊆ insert (0, 0) required_135 := by decide
theorem child_required_sub_135 : ∀ j, childrenC_135 j ⊆ insert (0, 0) required_135 := by decide
theorem child_envelope_sub_135 : ∀ j, childrenD_135 j ⊆ envelope_135 := by decide
theorem pivot_mem_135 : (0, 0) ∈ envelope_135 := by decide
theorem children_work_135 : ∀ j, Template HasSnaky 4 (childrenC_135 j) (childrenD_135 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 0 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_75 4 (-2, 1)).mono (by decide)
· exact (placed_template_map row_works_44 0 (1, 0)).mono (by decide)
theorem row_works_135 : Template HasSnaky 5 required_135 envelope_135 := by
refine compose HasSnaky 4 childrenC_135 childrenD_135 children_work_135 (0, 0)
required_135 envelope_135 pivot_mem_135 child_required_sub_135 child_envelope_sub_135 ?_
intro b hb; exact common_sub_135 (mem_commonEnvelope childrenD_135 b hb)
def required_136 : Finset Cell := ⟨(([(-2, -1), (-1, 2), (0, -1), (0, 1), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_136 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -2), (-1, -1), (-1, 0), (-1, 2), (-1, 3), (0, -1), (0, 0), (0, 1), (0, 2), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_136 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, 3) required_6), (placedSet 2 (-1, -1) required_102)]
def childrenD_136 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, 3) envelope_6), (placedSet 2 (-1, -1) envelope_102)]
theorem common_sub_136 : commonEnvelope childrenD_136 ⊆ insert (0, 0) required_136 := by decide
theorem child_required_sub_136 : ∀ j, childrenC_136 j ⊆ insert (0, 0) required_136 := by decide
theorem child_envelope_sub_136 : ∀ j, childrenD_136 j ⊆ envelope_136 := by decide
theorem pivot_mem_136 : (0, 0) ∈ envelope_136 := by decide
theorem children_work_136 : ∀ j, Template HasSnaky 4 (childrenC_136 j) (childrenD_136 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 3 (-1, 3)).mono (by decide)
· exact (placed_template_map row_works_102 2 (-1, -1)).mono (by decide)
theorem row_works_136 : Template HasSnaky 5 required_136 envelope_136 := by
refine compose HasSnaky 4 childrenC_136 childrenD_136 children_work_136 (0, 0)
required_136 envelope_136 pivot_mem_136 child_required_sub_136 child_envelope_sub_136 ?_
intro b hb; exact common_sub_136 (mem_commonEnvelope childrenD_136 b hb)
def required_140 : Finset Cell := ⟨(([(-1, -1), (-1, 1), (0, -1), (0, 1), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_140 : Finset Cell := ⟨(([(-3, 1), (-2, 1), (-1, -2), (-1, -1), (-1, 1), (0, -1), (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (1, 3), (2, 2), (3, 2)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_140 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -2) required_6), (placedSet 0 (1, 2) required_82)]
def childrenD_140 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -2) envelope_6), (placedSet 0 (1, 2) envelope_82)]
theorem common_sub_140 : commonEnvelope childrenD_140 ⊆ insert (0, 0) required_140 := by decide
theorem child_required_sub_140 : ∀ j, childrenC_140 j ⊆ insert (0, 0) required_140 := by decide
theorem child_envelope_sub_140 : ∀ j, childrenD_140 j ⊆ envelope_140 := by decide
theorem pivot_mem_140 : (0, 0) ∈ envelope_140 := by decide
theorem children_work_140 : ∀ j, Template HasSnaky 4 (childrenC_140 j) (childrenD_140 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 7 (-1, -2)).mono (by decide)
· exact (placed_template_map row_works_82 0 (1, 2)).mono (by decide)
theorem row_works_140 : Template HasSnaky 5 required_140 envelope_140 := by
refine compose HasSnaky 4 childrenC_140 childrenD_140 children_work_140 (0, 0)
required_140 envelope_140 pivot_mem_140 child_required_sub_140 child_envelope_sub_140 ?_
intro b hb; exact common_sub_140 (mem_commonEnvelope childrenD_140 b hb)
def required_142 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0), (-1, 1), (-1, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_142 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_142 : Fin 3 → Finset Cell := ![(placedSet 4 (-2, -1) required_72), (placedSet 1 (0, -1) required_32), (placedSet 2 (1, 0) required_55)]
def childrenD_142 : Fin 3 → Finset Cell := ![(placedSet 4 (-2, -1) envelope_72), (placedSet 1 (0, -1) envelope_32), (placedSet 2 (1, 0) envelope_55)]
theorem common_sub_142 : commonEnvelope childrenD_142 ⊆ insert (0, 0) required_142 := by decide
theorem child_required_sub_142 : ∀ j, childrenC_142 j ⊆ insert (0, 0) required_142 := by decide
theorem child_envelope_sub_142 : ∀ j, childrenD_142 j ⊆ envelope_142 := by decide
theorem pivot_mem_142 : (0, 0) ∈ envelope_142 := by decide
theorem children_work_142 : ∀ j, Template HasSnaky 4 (childrenC_142 j) (childrenD_142 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_72 4 (-2, -1)).mono (by decide)
· exact (placed_template_map row_works_32 1 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_55 2 (1, 0)).mono (by decide)
theorem row_works_142 : Template HasSnaky 5 required_142 envelope_142 := by
refine compose HasSnaky 4 childrenC_142 childrenD_142 children_work_142 (0, 0)
required_142 envelope_142 pivot_mem_142 child_required_sub_142 child_envelope_sub_142 ?_
intro b hb; exact common_sub_142 (mem_commonEnvelope childrenD_142 b hb)
end SnakyConditional
end OAI
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