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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.Level05Part02
import OAI.GameTheory.SnakyConditional.Templates.Level05Part03
import OAI.GameTheory.SnakyConditional.Templates.Level05Part06
namespace OAI
namespace SnakyConditional
def required_93 : Finset Cell := ⟨(([(1, -4), (1, -3), (1, -2), (1, -1), (2, 0), (3, -1), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_93 : Finset Cell := ⟨(([(0, -1), (0, 0), (0, 1), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0), (2, 0), (3, -1), (3, 0), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_93 : Fin 2 → Finset Cell := ![(placedSet 3 (0, -1) required_4), (placedSet 0 (1, 0) required_47)]
def childrenD_93 : Fin 2 → Finset Cell := ![(placedSet 3 (0, -1) envelope_4), (placedSet 0 (1, 0) envelope_47)]
theorem common_sub_93 : commonEnvelope childrenD_93 ⊆ insert (0, 0) required_93 := by decide
theorem child_required_sub_93 : ∀ j, childrenC_93 j ⊆ insert (0, 0) required_93 := by decide
theorem child_envelope_sub_93 : ∀ j, childrenD_93 j ⊆ envelope_93 := by decide
theorem pivot_mem_93 : (0, 0) ∈ envelope_93 := by decide
theorem children_work_93 : ∀ j, Template HasSnaky 3 (childrenC_93 j) (childrenD_93 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 3 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_47 0 (1, 0)).mono (by decide)
theorem row_works_93 : Template HasSnaky 4 required_93 envelope_93 := by
refine compose HasSnaky 3 childrenC_93 childrenD_93 children_work_93 (0, 0)
required_93 envelope_93 pivot_mem_93 child_required_sub_93 child_envelope_sub_93 ?_
intro b hb; exact common_sub_93 (mem_commonEnvelope childrenD_93 b hb)
def required_94 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_94 : Finset Cell := ⟨(([(-2, -2), (-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (0, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_94 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 3 (-1, 2) required_27)]
def childrenD_94 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 3 (-1, 2) envelope_27)]
theorem common_sub_94 : commonEnvelope childrenD_94 ⊆ insert (0, 0) required_94 := by decide
theorem child_required_sub_94 : ∀ j, childrenC_94 j ⊆ insert (0, 0) required_94 := by decide
theorem child_envelope_sub_94 : ∀ j, childrenD_94 j ⊆ envelope_94 := by decide
theorem pivot_mem_94 : (0, 0) ∈ envelope_94 := by decide
theorem children_work_94 : ∀ j, Template HasSnaky 3 (childrenC_94 j) (childrenD_94 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_27 3 (-1, 2)).mono (by decide)
theorem row_works_94 : Template HasSnaky 4 required_94 envelope_94 := by
refine compose HasSnaky 3 childrenC_94 childrenD_94 children_work_94 (0, 0)
required_94 envelope_94 pivot_mem_94 child_required_sub_94 child_envelope_sub_94 ?_
intro b hb; exact common_sub_94 (mem_commonEnvelope childrenD_94 b hb)
def required_95 : Finset Cell := ⟨(([(-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_95 : Finset Cell := ⟨(([(-2, 1), (-2, 2), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_95 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) required_0), (placedSet 0 (-2, 1) required_29)]
def childrenD_95 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) envelope_0), (placedSet 0 (-2, 1) envelope_29)]
theorem common_sub_95 : commonEnvelope childrenD_95 ⊆ insert (0, 0) required_95 := by decide
theorem child_required_sub_95 : ∀ j, childrenC_95 j ⊆ insert (0, 0) required_95 := by decide
theorem child_envelope_sub_95 : ∀ j, childrenD_95 j ⊆ envelope_95 := by decide
theorem pivot_mem_95 : (0, 0) ∈ envelope_95 := by decide
theorem children_work_95 : ∀ j, Template HasSnaky 3 (childrenC_95 j) (childrenD_95 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 5 (-1, 3)).mono (by decide)
· exact (placed_template_map row_works_29 0 (-2, 1)).mono (by decide)
theorem row_works_95 : Template HasSnaky 4 required_95 envelope_95 := by
refine compose HasSnaky 3 childrenC_95 childrenD_95 children_work_95 (0, 0)
required_95 envelope_95 pivot_mem_95 child_required_sub_95 child_envelope_sub_95 ?_
intro b hb; exact common_sub_95 (mem_commonEnvelope childrenD_95 b hb)
def required_99 : Finset Cell := ⟨(([(-2, -1), (-1, -4), (-1, -3), (-1, -1), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_99 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -4), (-1, -3), (-1, -2), (-1, -1), (0, -1), (0, 0), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_99 : Fin 2 → Finset Cell := ![(placedSet 1 (-1, -2) required_2), (placedSet 0 (1, 0) required_24)]
def childrenD_99 : Fin 2 → Finset Cell := ![(placedSet 1 (-1, -2) envelope_2), (placedSet 0 (1, 0) envelope_24)]
theorem common_sub_99 : commonEnvelope childrenD_99 ⊆ insert (0, 0) required_99 := by decide
theorem child_required_sub_99 : ∀ j, childrenC_99 j ⊆ insert (0, 0) required_99 := by decide
theorem child_envelope_sub_99 : ∀ j, childrenD_99 j ⊆ envelope_99 := by decide
theorem pivot_mem_99 : (0, 0) ∈ envelope_99 := by decide
theorem children_work_99 : ∀ j, Template HasSnaky 3 (childrenC_99 j) (childrenD_99 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_2 1 (-1, -2)).mono (by decide)
· exact (placed_template_map row_works_24 0 (1, 0)).mono (by decide)
theorem row_works_99 : Template HasSnaky 4 required_99 envelope_99 := by
refine compose HasSnaky 3 childrenC_99 childrenD_99 children_work_99 (0, 0)
required_99 envelope_99 pivot_mem_99 child_required_sub_99 child_envelope_sub_99 ?_
intro b hb; exact common_sub_99 (mem_commonEnvelope childrenD_99 b hb)
def required_100 : Finset Cell := ⟨(([(-3, -1), (-2, -3), (-2, -2), (-2, -1), (-2, 0), (-1, 0), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_100 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-3, 1), (-2, -3), (-2, -2), (-2, -1), (-2, 0), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_100 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) required_0), (placedSet 0 (-3, 0) required_48)]
def childrenD_100 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) envelope_0), (placedSet 0 (-3, 0) envelope_48)]
theorem common_sub_100 : commonEnvelope childrenD_100 ⊆ insert (0, 0) required_100 := by decide
theorem child_required_sub_100 : ∀ j, childrenC_100 j ⊆ insert (0, 0) required_100 := by decide
theorem child_envelope_sub_100 : ∀ j, childrenD_100 j ⊆ envelope_100 := by decide
theorem pivot_mem_100 : (0, 0) ∈ envelope_100 := by decide
theorem children_work_100 : ∀ j, Template HasSnaky 3 (childrenC_100 j) (childrenD_100 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 6 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_48 0 (-3, 0)).mono (by decide)
theorem row_works_100 : Template HasSnaky 4 required_100 envelope_100 := by
refine compose HasSnaky 3 childrenC_100 childrenD_100 children_work_100 (0, 0)
required_100 envelope_100 pivot_mem_100 child_required_sub_100 child_envelope_sub_100 ?_
intro b hb; exact common_sub_100 (mem_commonEnvelope childrenD_100 b hb)
def required_101 : Finset Cell := ⟨(([(-2, -1), (-1, -2), (-1, -1), (0, -1), (0, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_101 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -2), (-1, -1), (0, -1), (0, 0), (0, 1), (0, 2), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_101 : Fin 2 → Finset Cell := ![(placedSet 7 (0, 2) required_0), (placedSet 0 (1, 0) required_24)]
def childrenD_101 : Fin 2 → Finset Cell := ![(placedSet 7 (0, 2) envelope_0), (placedSet 0 (1, 0) envelope_24)]
theorem common_sub_101 : commonEnvelope childrenD_101 ⊆ insert (0, 0) required_101 := by decide
theorem child_required_sub_101 : ∀ j, childrenC_101 j ⊆ insert (0, 0) required_101 := by decide
theorem child_envelope_sub_101 : ∀ j, childrenD_101 j ⊆ envelope_101 := by decide
theorem pivot_mem_101 : (0, 0) ∈ envelope_101 := by decide
theorem children_work_101 : ∀ j, Template HasSnaky 3 (childrenC_101 j) (childrenD_101 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 0 (1, 0)).mono (by decide)
theorem row_works_101 : Template HasSnaky 4 required_101 envelope_101 := by
refine compose HasSnaky 3 childrenC_101 childrenD_101 children_work_101 (0, 0)
required_101 envelope_101 pivot_mem_101 child_required_sub_101 child_envelope_sub_101 ?_
intro b hb; exact common_sub_101 (mem_commonEnvelope childrenD_101 b hb)
def required_102 : Finset Cell := ⟨(([(-1, 0), (1, -3), (1, -2), (1, -1), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_102 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, -1), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_102 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 2 (2, -1) required_25)]
def childrenD_102 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 2 (2, -1) envelope_25)]
theorem common_sub_102 : commonEnvelope childrenD_102 ⊆ insert (0, 0) required_102 := by decide
theorem child_required_sub_102 : ∀ j, childrenC_102 j ⊆ insert (0, 0) required_102 := by decide
theorem child_envelope_sub_102 : ∀ j, childrenD_102 j ⊆ envelope_102 := by decide
theorem pivot_mem_102 : (0, 0) ∈ envelope_102 := by decide
theorem children_work_102 : ∀ j, Template HasSnaky 3 (childrenC_102 j) (childrenD_102 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_25 2 (2, -1)).mono (by decide)
theorem row_works_102 : Template HasSnaky 4 required_102 envelope_102 := by
refine compose HasSnaky 3 childrenC_102 childrenD_102 children_work_102 (0, 0)
required_102 envelope_102 pivot_mem_102 child_required_sub_102 child_envelope_sub_102 ?_
intro b hb; exact common_sub_102 (mem_commonEnvelope childrenD_102 b hb)
end SnakyConditional
end OAI
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