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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 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part01
import OAI.GameTheory.SnakyConditional.Templates.Level06Part02
import OAI.GameTheory.SnakyConditional.Templates.Level06Part06
namespace OAI
namespace SnakyConditional
def required_120 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_120 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_120 : Fin 2 → Finset Cell := ![(placedSet 0 (0, 1) required_4), (placedSet 2 (1, 0) required_58)]
def childrenD_120 : Fin 2 → Finset Cell := ![(placedSet 0 (0, 1) envelope_4), (placedSet 2 (1, 0) envelope_58)]
theorem common_sub_120 : commonEnvelope childrenD_120 ⊆ insert (0, 0) required_120 := by decide
theorem child_required_sub_120 : ∀ j, childrenC_120 j ⊆ insert (0, 0) required_120 := by decide
theorem child_envelope_sub_120 : ∀ j, childrenD_120 j ⊆ envelope_120 := by decide
theorem pivot_mem_120 : (0, 0) ∈ envelope_120 := by decide
theorem children_work_120 : ∀ j, Template HasSnaky 4 (childrenC_120 j) (childrenD_120 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 0 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_58 2 (1, 0)).mono (by decide)
theorem row_works_120 : Template HasSnaky 5 required_120 envelope_120 := by
refine compose HasSnaky 4 childrenC_120 childrenD_120 children_work_120 (0, 0)
required_120 envelope_120 pivot_mem_120 child_required_sub_120 child_envelope_sub_120 ?_
intro b hb; exact common_sub_120 (mem_commonEnvelope childrenD_120 b hb)
def required_122 : Finset Cell := ⟨(([(0, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_122 : Finset Cell := ⟨(([(-1, -1), (-1, 1), (0, -2), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (3, 0), (4, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_122 : Fin 2 → Finset Cell := ![(placedSet 6 (-1, -1) required_6), (placedSet 1 (0, 1) required_105)]
def childrenD_122 : Fin 2 → Finset Cell := ![(placedSet 6 (-1, -1) envelope_6), (placedSet 1 (0, 1) envelope_105)]
theorem common_sub_122 : commonEnvelope childrenD_122 ⊆ insert (0, 0) required_122 := by decide
theorem child_required_sub_122 : ∀ j, childrenC_122 j ⊆ insert (0, 0) required_122 := by decide
theorem child_envelope_sub_122 : ∀ j, childrenD_122 j ⊆ envelope_122 := by decide
theorem pivot_mem_122 : (0, 0) ∈ envelope_122 := by decide
theorem children_work_122 : ∀ j, Template HasSnaky 4 (childrenC_122 j) (childrenD_122 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 6 (-1, -1)).mono (by decide)
· exact (placed_template_map row_works_105 1 (0, 1)).mono (by decide)
theorem row_works_122 : Template HasSnaky 5 required_122 envelope_122 := by
refine compose HasSnaky 4 childrenC_122 childrenD_122 children_work_122 (0, 0)
required_122 envelope_122 pivot_mem_122 child_required_sub_122 child_envelope_sub_122 ?_
intro b hb; exact common_sub_122 (mem_commonEnvelope childrenD_122 b hb)
def required_126 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_126 : Finset Cell := ⟨(([(0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (2, 4)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_126 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 1 (1, 3) required_46)]
def childrenD_126 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 1 (1, 3) envelope_46)]
theorem common_sub_126 : commonEnvelope childrenD_126 ⊆ insert (0, 0) required_126 := by decide
theorem child_required_sub_126 : ∀ j, childrenC_126 j ⊆ insert (0, 0) required_126 := by decide
theorem child_envelope_sub_126 : ∀ j, childrenD_126 j ⊆ envelope_126 := by decide
theorem pivot_mem_126 : (0, 0) ∈ envelope_126 := by decide
theorem children_work_126 : ∀ j, Template HasSnaky 4 (childrenC_126 j) (childrenD_126 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_46 1 (1, 3)).mono (by decide)
theorem row_works_126 : Template HasSnaky 5 required_126 envelope_126 := by
refine compose HasSnaky 4 childrenC_126 childrenD_126 children_work_126 (0, 0)
required_126 envelope_126 pivot_mem_126 child_required_sub_126 child_envelope_sub_126 ?_
intro b hb; exact common_sub_126 (mem_commonEnvelope childrenD_126 b hb)
def required_127 : Finset Cell := ⟨(([(-4, 0), (-3, -1), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_127 : Finset Cell := ⟨(([(-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_127 : Fin 2 → Finset Cell := ![(placedSet 0 (0, 1) required_7), (placedSet 2 (1, 0) required_44)]
def childrenD_127 : Fin 2 → Finset Cell := ![(placedSet 0 (0, 1) envelope_7), (placedSet 2 (1, 0) envelope_44)]
theorem common_sub_127 : commonEnvelope childrenD_127 ⊆ insert (0, 0) required_127 := by decide
theorem child_required_sub_127 : ∀ j, childrenC_127 j ⊆ insert (0, 0) required_127 := by decide
theorem child_envelope_sub_127 : ∀ j, childrenD_127 j ⊆ envelope_127 := by decide
theorem pivot_mem_127 : (0, 0) ∈ envelope_127 := by decide
theorem children_work_127 : ∀ j, Template HasSnaky 4 (childrenC_127 j) (childrenD_127 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_44 2 (1, 0)).mono (by decide)
theorem row_works_127 : Template HasSnaky 5 required_127 envelope_127 := by
refine compose HasSnaky 4 childrenC_127 childrenD_127 children_work_127 (0, 0)
required_127 envelope_127 pivot_mem_127 child_required_sub_127 child_envelope_sub_127 ?_
intro b hb; exact common_sub_127 (mem_commonEnvelope childrenD_127 b hb)
def required_128 : Finset Cell := ⟨(([(-2, 1), (-1, 0), (-1, 1), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_128 : Finset Cell := ⟨(([(-4, 1), (-3, 1), (-2, 1), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_128 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, 1) required_9), (placedSet 0 (2, 1) required_57)]
def childrenD_128 : Fin 2 → Finset Cell := ![(placedSet 6 (-3, 1) envelope_9), (placedSet 0 (2, 1) envelope_57)]
theorem common_sub_128 : commonEnvelope childrenD_128 ⊆ insert (0, 0) required_128 := by decide
theorem child_required_sub_128 : ∀ j, childrenC_128 j ⊆ insert (0, 0) required_128 := by decide
theorem child_envelope_sub_128 : ∀ j, childrenD_128 j ⊆ envelope_128 := by decide
theorem pivot_mem_128 : (0, 0) ∈ envelope_128 := by decide
theorem children_work_128 : ∀ j, Template HasSnaky 4 (childrenC_128 j) (childrenD_128 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_9 6 (-3, 1)).mono (by decide)
· exact (placed_template_map row_works_57 0 (2, 1)).mono (by decide)
theorem row_works_128 : Template HasSnaky 5 required_128 envelope_128 := by
refine compose HasSnaky 4 childrenC_128 childrenD_128 children_work_128 (0, 0)
required_128 envelope_128 pivot_mem_128 child_required_sub_128 child_envelope_sub_128 ?_
intro b hb; exact common_sub_128 (mem_commonEnvelope childrenD_128 b hb)
def required_129 : Finset Cell := ⟨(([(-1, -2), (-1, -1), (-1, 0), (-1, 1), (0, -1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_129 : Finset Cell := ⟨(([(-2, 1), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_129 : Fin 2 → Finset Cell := ![(placedSet 4 (-2, 1) required_6), (placedSet 1 (-1, 2) required_58)]
def childrenD_129 : Fin 2 → Finset Cell := ![(placedSet 4 (-2, 1) envelope_6), (placedSet 1 (-1, 2) envelope_58)]
theorem common_sub_129 : commonEnvelope childrenD_129 ⊆ insert (0, 0) required_129 := by decide
theorem child_required_sub_129 : ∀ j, childrenC_129 j ⊆ insert (0, 0) required_129 := by decide
theorem child_envelope_sub_129 : ∀ j, childrenD_129 j ⊆ envelope_129 := by decide
theorem pivot_mem_129 : (0, 0) ∈ envelope_129 := by decide
theorem children_work_129 : ∀ j, Template HasSnaky 4 (childrenC_129 j) (childrenD_129 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 4 (-2, 1)).mono (by decide)
· exact (placed_template_map row_works_58 1 (-1, 2)).mono (by decide)
theorem row_works_129 : Template HasSnaky 5 required_129 envelope_129 := by
refine compose HasSnaky 4 childrenC_129 childrenD_129 children_work_129 (0, 0)
required_129 envelope_129 pivot_mem_129 child_required_sub_129 child_envelope_sub_129 ?_
intro b hb; exact common_sub_129 (mem_commonEnvelope childrenD_129 b hb)
def required_131 : Finset Cell := ⟨(([(-1, -2), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_131 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, 0), (-1, 1), (-1, 2), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_131 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_45), (placedSet 1 (1, 0) required_7)]
def childrenD_131 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_45), (placedSet 1 (1, 0) envelope_7)]
theorem common_sub_131 : commonEnvelope childrenD_131 ⊆ insert (0, 0) required_131 := by decide
theorem child_required_sub_131 : ∀ j, childrenC_131 j ⊆ insert (0, 0) required_131 := by decide
theorem child_envelope_sub_131 : ∀ j, childrenD_131 j ⊆ envelope_131 := by decide
theorem pivot_mem_131 : (0, 0) ∈ envelope_131 := by decide
theorem children_work_131 : ∀ j, Template HasSnaky 4 (childrenC_131 j) (childrenD_131 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_45 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
theorem row_works_131 : Template HasSnaky 5 required_131 envelope_131 := by
refine compose HasSnaky 4 childrenC_131 childrenD_131 children_work_131 (0, 0)
required_131 envelope_131 pivot_mem_131 child_required_sub_131 child_envelope_sub_131 ?_
intro b hb; exact common_sub_131 (mem_commonEnvelope childrenD_131 b hb)
end SnakyConditional
end OAI
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