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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.Level03Part02
import OAI.GameTheory.SnakyConditional.Templates.Level05Part01
import OAI.GameTheory.SnakyConditional.Templates.Level05Part02
import OAI.GameTheory.SnakyConditional.Templates.Level05Part05
import OAI.GameTheory.SnakyConditional.Templates.Level05Part07
import OAI.GameTheory.SnakyConditional.Templates.Level05Part08
namespace OAI
namespace SnakyConditional
def required_103 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_103 : Finset Cell := ⟨(([(-1, 0), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, -1), (2, 0), (2, 1), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_103 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 0 (2, 0) required_71)]
def childrenD_103 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 0 (2, 0) envelope_71)]
theorem common_sub_103 : commonEnvelope childrenD_103 ⊆ insert (0, 0) required_103 := by decide
theorem child_required_sub_103 : ∀ j, childrenC_103 j ⊆ insert (0, 0) required_103 := by decide
theorem child_envelope_sub_103 : ∀ j, childrenD_103 j ⊆ envelope_103 := by decide
theorem pivot_mem_103 : (0, 0) ∈ envelope_103 := by decide
theorem children_work_103 : ∀ j, Template HasSnaky 3 (childrenC_103 j) (childrenD_103 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_71 0 (2, 0)).mono (by decide)
theorem row_works_103 : Template HasSnaky 4 required_103 envelope_103 := by
refine compose HasSnaky 3 childrenC_103 childrenD_103 children_work_103 (0, 0)
required_103 envelope_103 pivot_mem_103 child_required_sub_103 child_envelope_sub_103 ?_
intro b hb; exact common_sub_103 (mem_commonEnvelope childrenD_103 b hb)
def required_105 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (-1, 1), (-1, 2), (-1, 3)] : List Cell) : Multiset Cell), by decide⟩
def envelope_105 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (-1, 4), (0, -1), (0, 0), (0, 1), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_105 : Fin 2 → Finset Cell := ![(placedSet 5 (0, -1) required_6), (placedSet 0 (0, 1) required_77)]
def childrenD_105 : Fin 2 → Finset Cell := ![(placedSet 5 (0, -1) envelope_6), (placedSet 0 (0, 1) envelope_77)]
theorem common_sub_105 : commonEnvelope childrenD_105 ⊆ insert (0, 0) required_105 := by decide
theorem child_required_sub_105 : ∀ j, childrenC_105 j ⊆ insert (0, 0) required_105 := by decide
theorem child_envelope_sub_105 : ∀ j, childrenD_105 j ⊆ envelope_105 := by decide
theorem pivot_mem_105 : (0, 0) ∈ envelope_105 := by decide
theorem children_work_105 : ∀ j, Template HasSnaky 3 (childrenC_105 j) (childrenD_105 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 5 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_77 0 (0, 1)).mono (by decide)
theorem row_works_105 : Template HasSnaky 4 required_105 envelope_105 := by
refine compose HasSnaky 3 childrenC_105 childrenD_105 children_work_105 (0, 0)
required_105 envelope_105 pivot_mem_105 child_required_sub_105 child_envelope_sub_105 ?_
intro b hb; exact common_sub_105 (mem_commonEnvelope childrenD_105 b hb)
def required_106 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_106 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_106 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 6 (1, 0) required_36)]
def childrenD_106 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 6 (1, 0) envelope_36)]
theorem common_sub_106 : commonEnvelope childrenD_106 ⊆ insert (0, 0) required_106 := by decide
theorem child_required_sub_106 : ∀ j, childrenC_106 j ⊆ insert (0, 0) required_106 := by decide
theorem child_envelope_sub_106 : ∀ j, childrenD_106 j ⊆ envelope_106 := by decide
theorem pivot_mem_106 : (0, 0) ∈ envelope_106 := by decide
theorem children_work_106 : ∀ j, Template HasSnaky 3 (childrenC_106 j) (childrenD_106 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_36 6 (1, 0)).mono (by decide)
theorem row_works_106 : Template HasSnaky 4 required_106 envelope_106 := by
refine compose HasSnaky 3 childrenC_106 childrenD_106 children_work_106 (0, 0)
required_106 envelope_106 pivot_mem_106 child_required_sub_106 child_envelope_sub_106 ?_
intro b hb; exact common_sub_106 (mem_commonEnvelope childrenD_106 b hb)
def required_113 : Finset Cell := ⟨(([(-1, -1), (0, -1), (1, 0), (1, 1), (2, 1), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_113 : Finset Cell := ⟨(([(-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_113 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) required_1), (placedSet 6 (3, 1) required_36)]
def childrenD_113 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) envelope_1), (placedSet 6 (3, 1) envelope_36)]
theorem common_sub_113 : commonEnvelope childrenD_113 ⊆ insert (0, 0) required_113 := by decide
theorem child_required_sub_113 : ∀ j, childrenC_113 j ⊆ insert (0, 0) required_113 := by decide
theorem child_envelope_sub_113 : ∀ j, childrenD_113 j ⊆ envelope_113 := by decide
theorem pivot_mem_113 : (0, 0) ∈ envelope_113 := by decide
theorem children_work_113 : ∀ j, Template HasSnaky 3 (childrenC_113 j) (childrenD_113 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_1 6 (2, 0)).mono (by decide)
· exact (placed_template_map row_works_36 6 (3, 1)).mono (by decide)
theorem row_works_113 : Template HasSnaky 4 required_113 envelope_113 := by
refine compose HasSnaky 3 childrenC_113 childrenD_113 children_work_113 (0, 0)
required_113 envelope_113 pivot_mem_113 child_required_sub_113 child_envelope_sub_113 ?_
intro b hb; exact common_sub_113 (mem_commonEnvelope childrenD_113 b hb)
def required_116 : Finset Cell := ⟨(([(-2, 1), (-1, -2), (-1, -1), (-1, 1), (0, -1), (0, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_116 : Finset Cell := ⟨(([(-3, 1), (-2, 1), (-1, -2), (-1, -1), (-1, 1), (0, -1), (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_116 : Fin 2 → Finset Cell := ![(placedSet 7 (0, 2) required_0), (placedSet 2 (1, 0) required_24)]
def childrenD_116 : Fin 2 → Finset Cell := ![(placedSet 7 (0, 2) envelope_0), (placedSet 2 (1, 0) envelope_24)]
theorem common_sub_116 : commonEnvelope childrenD_116 ⊆ insert (0, 0) required_116 := by decide
theorem child_required_sub_116 : ∀ j, childrenC_116 j ⊆ insert (0, 0) required_116 := by decide
theorem child_envelope_sub_116 : ∀ j, childrenD_116 j ⊆ envelope_116 := by decide
theorem pivot_mem_116 : (0, 0) ∈ envelope_116 := by decide
theorem children_work_116 : ∀ j, Template HasSnaky 3 (childrenC_116 j) (childrenD_116 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 7 (0, 2)).mono (by decide)
· exact (placed_template_map row_works_24 2 (1, 0)).mono (by decide)
theorem row_works_116 : Template HasSnaky 4 required_116 envelope_116 := by
refine compose HasSnaky 3 childrenC_116 childrenD_116 children_work_116 (0, 0)
required_116 envelope_116 pivot_mem_116 child_required_sub_116 child_envelope_sub_116 ?_
intro b hb; exact common_sub_116 (mem_commonEnvelope childrenD_116 b hb)
def required_118 : Finset Cell := ⟨(([(-2, -1), (-1, -4), (-1, -1), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_118 : Finset Cell := ⟨(([(-2, -1), (-1, -4), (-1, -3), (-1, -1), (-1, 0), (0, -3), (0, -2), (0, -1), (0, 0), (1, 0), (1, 1), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_118 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -3) required_4), (placedSet 1 (1, 0) required_61)]
def childrenD_118 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -3) envelope_4), (placedSet 1 (1, 0) envelope_61)]
theorem common_sub_118 : commonEnvelope childrenD_118 ⊆ insert (0, 0) required_118 := by decide
theorem child_required_sub_118 : ∀ j, childrenC_118 j ⊆ insert (0, 0) required_118 := by decide
theorem child_envelope_sub_118 : ∀ j, childrenD_118 j ⊆ envelope_118 := by decide
theorem pivot_mem_118 : (0, 0) ∈ envelope_118 := by decide
theorem children_work_118 : ∀ j, Template HasSnaky 3 (childrenC_118 j) (childrenD_118 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 7 (-1, -3)).mono (by decide)
· exact (placed_template_map row_works_61 1 (1, 0)).mono (by decide)
theorem row_works_118 : Template HasSnaky 4 required_118 envelope_118 := by
refine compose HasSnaky 3 childrenC_118 childrenD_118 children_work_118 (0, 0)
required_118 envelope_118 pivot_mem_118 child_required_sub_118 child_envelope_sub_118 ?_
intro b hb; exact common_sub_118 (mem_commonEnvelope childrenD_118 b hb)
def required_121 : Finset Cell := ⟨(([(-1, -2), (-1, -1), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_121 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_121 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_9), (placedSet 1 (1, 0) required_7)]
def childrenD_121 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_9), (placedSet 1 (1, 0) envelope_7)]
theorem common_sub_121 : commonEnvelope childrenD_121 ⊆ insert (0, 0) required_121 := by decide
theorem child_required_sub_121 : ∀ j, childrenC_121 j ⊆ insert (0, 0) required_121 := by decide
theorem child_envelope_sub_121 : ∀ j, childrenD_121 j ⊆ envelope_121 := by decide
theorem pivot_mem_121 : (0, 0) ∈ envelope_121 := by decide
theorem children_work_121 : ∀ j, Template HasSnaky 3 (childrenC_121 j) (childrenD_121 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_9 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
theorem row_works_121 : Template HasSnaky 4 required_121 envelope_121 := by
refine compose HasSnaky 3 childrenC_121 childrenD_121 children_work_121 (0, 0)
required_121 envelope_121 pivot_mem_121 child_required_sub_121 child_envelope_sub_121 ?_
intro b hb; exact common_sub_121 (mem_commonEnvelope childrenD_121 b hb)
end SnakyConditional
end OAI
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