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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 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part01
import OAI.GameTheory.SnakyConditional.Templates.Level06Part02
import OAI.GameTheory.SnakyConditional.Templates.Level06Part03
import OAI.GameTheory.SnakyConditional.Templates.Level06Part05
namespace OAI
namespace SnakyConditional
def required_104 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (0, -1), (1, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_104 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_104 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) required_6), (placedSet 0 (-1, 0) required_75)]
def childrenD_104 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) envelope_6), (placedSet 0 (-1, 0) envelope_75)]
theorem common_sub_104 : commonEnvelope childrenD_104 ⊆ insert (0, 0) required_104 := by decide
theorem child_required_sub_104 : ∀ j, childrenC_104 j ⊆ insert (0, 0) required_104 := by decide
theorem child_envelope_sub_104 : ∀ j, childrenD_104 j ⊆ envelope_104 := by decide
theorem pivot_mem_104 : (0, 0) ∈ envelope_104 := by decide
theorem children_work_104 : ∀ j, Template HasSnaky 4 (childrenC_104 j) (childrenD_104 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_75 0 (-1, 0)).mono (by decide)
theorem row_works_104 : Template HasSnaky 5 required_104 envelope_104 := by
refine compose HasSnaky 4 childrenC_104 childrenD_104 children_work_104 (0, 0)
required_104 envelope_104 pivot_mem_104 child_required_sub_104 child_envelope_sub_104 ?_
intro b hb; exact common_sub_104 (mem_commonEnvelope childrenD_104 b hb)
def required_109 : Finset Cell := ⟨(([(-4, -1), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_109 : Finset Cell := ⟨(([(-4, -1), (-4, 1), (-3, -1), (-3, 0), (-3, 1), (-2, 0), (-2, 1), (-1, 0), (0, 0), (0, 1), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_109 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) required_4), (placedSet 0 (1, 0) required_55)]
def childrenD_109 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) envelope_4), (placedSet 0 (1, 0) envelope_55)]
theorem common_sub_109 : commonEnvelope childrenD_109 ⊆ insert (0, 0) required_109 := by decide
theorem child_required_sub_109 : ∀ j, childrenC_109 j ⊆ insert (0, 0) required_109 := by decide
theorem child_envelope_sub_109 : ∀ j, childrenD_109 j ⊆ envelope_109 := by decide
theorem pivot_mem_109 : (0, 0) ∈ envelope_109 := by decide
theorem children_work_109 : ∀ j, Template HasSnaky 4 (childrenC_109 j) (childrenD_109 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 6 (-3, -1)).mono (by decide)
· exact (placed_template_map row_works_55 0 (1, 0)).mono (by decide)
theorem row_works_109 : Template HasSnaky 5 required_109 envelope_109 := by
refine compose HasSnaky 4 childrenC_109 childrenD_109 children_work_109 (0, 0)
required_109 envelope_109 pivot_mem_109 child_required_sub_109 child_envelope_sub_109 ?_
intro b hb; exact common_sub_109 (mem_commonEnvelope childrenD_109 b hb)
def required_112 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, 1), (2, 0), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_112 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_112 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 0) required_4), (placedSet 0 (-1, 1) required_93)]
def childrenD_112 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 0) envelope_4), (placedSet 0 (-1, 1) envelope_93)]
theorem common_sub_112 : commonEnvelope childrenD_112 ⊆ insert (0, 0) required_112 := by decide
theorem child_required_sub_112 : ∀ j, childrenC_112 j ⊆ insert (0, 0) required_112 := by decide
theorem child_envelope_sub_112 : ∀ j, childrenD_112 j ⊆ envelope_112 := by decide
theorem pivot_mem_112 : (0, 0) ∈ envelope_112 := by decide
theorem children_work_112 : ∀ j, Template HasSnaky 4 (childrenC_112 j) (childrenD_112 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 1 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_93 0 (-1, 1)).mono (by decide)
theorem row_works_112 : Template HasSnaky 5 required_112 envelope_112 := by
refine compose HasSnaky 4 childrenC_112 childrenD_112 children_work_112 (0, 0)
required_112 envelope_112 pivot_mem_112 child_required_sub_112 child_envelope_sub_112 ?_
intro b hb; exact common_sub_112 (mem_commonEnvelope childrenD_112 b hb)
def required_114 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, -1), (-1, 0), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_114 : Finset Cell := ⟨(([(-3, 1), (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-2, 3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_114 : Fin 2 → Finset Cell := ![(placedSet 0 (2, 1) required_6), (placedSet 3 (-2, 1) required_67)]
def childrenD_114 : Fin 2 → Finset Cell := ![(placedSet 0 (2, 1) envelope_6), (placedSet 3 (-2, 1) envelope_67)]
theorem common_sub_114 : commonEnvelope childrenD_114 ⊆ insert (0, 0) required_114 := by decide
theorem child_required_sub_114 : ∀ j, childrenC_114 j ⊆ insert (0, 0) required_114 := by decide
theorem child_envelope_sub_114 : ∀ j, childrenD_114 j ⊆ envelope_114 := by decide
theorem pivot_mem_114 : (0, 0) ∈ envelope_114 := by decide
theorem children_work_114 : ∀ j, Template HasSnaky 4 (childrenC_114 j) (childrenD_114 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 0 (2, 1)).mono (by decide)
· exact (placed_template_map row_works_67 3 (-2, 1)).mono (by decide)
theorem row_works_114 : Template HasSnaky 5 required_114 envelope_114 := by
refine compose HasSnaky 4 childrenC_114 childrenD_114 children_work_114 (0, 0)
required_114 envelope_114 pivot_mem_114 child_required_sub_114 child_envelope_sub_114 ?_
intro b hb; exact common_sub_114 (mem_commonEnvelope childrenD_114 b hb)
def required_115 : Finset Cell := ⟨(([(-1, -3), (-1, -1), (-1, 0), (1, 0), (2, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_115 : Finset Cell := ⟨(([(-3, 1), (-2, 0), (-2, 1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (0, 0), (1, 0), (2, -1), (2, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_115 : Fin 2 → Finset Cell := ![(placedSet 2 (3, -1) required_6), (placedSet 7 (-2, 1) required_70)]
def childrenD_115 : Fin 2 → Finset Cell := ![(placedSet 2 (3, -1) envelope_6), (placedSet 7 (-2, 1) envelope_70)]
theorem common_sub_115 : commonEnvelope childrenD_115 ⊆ insert (0, 0) required_115 := by decide
theorem child_required_sub_115 : ∀ j, childrenC_115 j ⊆ insert (0, 0) required_115 := by decide
theorem child_envelope_sub_115 : ∀ j, childrenD_115 j ⊆ envelope_115 := by decide
theorem pivot_mem_115 : (0, 0) ∈ envelope_115 := by decide
theorem children_work_115 : ∀ j, Template HasSnaky 4 (childrenC_115 j) (childrenD_115 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 2 (3, -1)).mono (by decide)
· exact (placed_template_map row_works_70 7 (-2, 1)).mono (by decide)
theorem row_works_115 : Template HasSnaky 5 required_115 envelope_115 := by
refine compose HasSnaky 4 childrenC_115 childrenD_115 children_work_115 (0, 0)
required_115 envelope_115 pivot_mem_115 child_required_sub_115 child_envelope_sub_115 ?_
intro b hb; exact common_sub_115 (mem_commonEnvelope childrenD_115 b hb)
def required_117 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (1, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_117 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-2, 1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, -1), (1, 0), (2, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_117 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 0 (1, 0) required_100)]
def childrenD_117 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 0 (1, 0) envelope_100)]
theorem common_sub_117 : commonEnvelope childrenD_117 ⊆ insert (0, 0) required_117 := by decide
theorem child_required_sub_117 : ∀ j, childrenC_117 j ⊆ insert (0, 0) required_117 := by decide
theorem child_envelope_sub_117 : ∀ j, childrenD_117 j ⊆ envelope_117 := by decide
theorem pivot_mem_117 : (0, 0) ∈ envelope_117 := by decide
theorem children_work_117 : ∀ j, Template HasSnaky 4 (childrenC_117 j) (childrenD_117 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_100 0 (1, 0)).mono (by decide)
theorem row_works_117 : Template HasSnaky 5 required_117 envelope_117 := by
refine compose HasSnaky 4 childrenC_117 childrenD_117 children_work_117 (0, 0)
required_117 envelope_117 pivot_mem_117 child_required_sub_117 child_envelope_sub_117 ?_
intro b hb; exact common_sub_117 (mem_commonEnvelope childrenD_117 b hb)
def required_119 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_119 : Finset Cell := ⟨(([(-3, -1), (-3, 1), (-2, -1), (-2, 0), (-2, 1), (-1, 0), (-1, 1), (0, 0), (1, 0), (1, 1), (2, 0), (2, 1), (3, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_119 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) required_6), (placedSet 0 (2, 0) required_55)]
def childrenD_119 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, -1) envelope_6), (placedSet 0 (2, 0) envelope_55)]
theorem common_sub_119 : commonEnvelope childrenD_119 ⊆ insert (0, 0) required_119 := by decide
theorem child_required_sub_119 : ∀ j, childrenC_119 j ⊆ insert (0, 0) required_119 := by decide
theorem child_envelope_sub_119 : ∀ j, childrenD_119 j ⊆ envelope_119 := by decide
theorem pivot_mem_119 : (0, 0) ∈ envelope_119 := by decide
theorem children_work_119 : ∀ j, Template HasSnaky 4 (childrenC_119 j) (childrenD_119 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 6 (-3, -1)).mono (by decide)
· exact (placed_template_map row_works_55 0 (2, 0)).mono (by decide)
theorem row_works_119 : Template HasSnaky 5 required_119 envelope_119 := by
refine compose HasSnaky 4 childrenC_119 childrenD_119 children_work_119 (0, 0)
required_119 envelope_119 pivot_mem_119 child_required_sub_119 child_envelope_sub_119 ?_
intro b hb; exact common_sub_119 (mem_commonEnvelope childrenD_119 b hb)
end SnakyConditional
end OAI
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