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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 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part01
import OAI.GameTheory.SnakyConditional.Templates.Level06Part02
import OAI.GameTheory.SnakyConditional.Templates.Level06Part05
namespace OAI
namespace SnakyConditional
def required_147 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-2, 0), (-2, 2), (-2, 3), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_147 : Finset Cell := ⟨(([(-4, 1), (-3, -1), (-3, 0), (-3, 1), (-3, 2), (-2, -1), (-2, 0), (-2, 2), (-2, 3), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_147 : Fin 2 → Finset Cell := ![(placedSet 0 (-3, 1) required_53), (placedSet 2 (1, 0) required_44)]
def childrenD_147 : Fin 2 → Finset Cell := ![(placedSet 0 (-3, 1) envelope_53), (placedSet 2 (1, 0) envelope_44)]
theorem common_sub_147 : commonEnvelope childrenD_147 ⊆ insert (0, 0) required_147 := by decide
theorem child_required_sub_147 : ∀ j, childrenC_147 j ⊆ insert (0, 0) required_147 := by decide
theorem child_envelope_sub_147 : ∀ j, childrenD_147 j ⊆ envelope_147 := by decide
theorem pivot_mem_147 : (0, 0) ∈ envelope_147 := by decide
theorem children_work_147 : ∀ j, Template HasSnaky 4 (childrenC_147 j) (childrenD_147 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_53 0 (-3, 1)).mono (by decide)
· exact (placed_template_map row_works_44 2 (1, 0)).mono (by decide)
theorem row_works_147 : Template HasSnaky 5 required_147 envelope_147 := by
refine compose HasSnaky 4 childrenC_147 childrenD_147 children_work_147 (0, 0)
required_147 envelope_147 pivot_mem_147 child_required_sub_147 child_envelope_sub_147 ?_
intro b hb; exact common_sub_147 (mem_commonEnvelope childrenD_147 b hb)
def required_151 : Finset Cell := ⟨(([(0, -3), (0, -2), (1, 0), (1, 1), (2, -2), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_151 : Finset Cell := ⟨(([(-1, 0), (0, -3), (0, -2), (0, -1), (0, 0), (1, 0), (1, 1), (2, -3), (2, -2), (2, -1), (2, 0), (3, -1), (3, 0), (4, -1), (5, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_151 : Fin 2 → Finset Cell := ![(placedSet 1 (0, -1) required_2), (placedSet 2 (2, -1) required_101)]
def childrenD_151 : Fin 2 → Finset Cell := ![(placedSet 1 (0, -1) envelope_2), (placedSet 2 (2, -1) envelope_101)]
theorem common_sub_151 : commonEnvelope childrenD_151 ⊆ insert (0, 0) required_151 := by decide
theorem child_required_sub_151 : ∀ j, childrenC_151 j ⊆ insert (0, 0) required_151 := by decide
theorem child_envelope_sub_151 : ∀ j, childrenD_151 j ⊆ envelope_151 := by decide
theorem pivot_mem_151 : (0, 0) ∈ envelope_151 := by decide
theorem children_work_151 : ∀ j, Template HasSnaky 4 (childrenC_151 j) (childrenD_151 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_2 1 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_101 2 (2, -1)).mono (by decide)
theorem row_works_151 : Template HasSnaky 5 required_151 envelope_151 := by
refine compose HasSnaky 4 childrenC_151 childrenD_151 children_work_151 (0, 0)
required_151 envelope_151 pivot_mem_151 child_required_sub_151 child_envelope_sub_151 ?_
intro b hb; exact common_sub_151 (mem_commonEnvelope childrenD_151 b hb)
def required_153 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_153 : Finset Cell := ⟨(([(-5, 0), (-4, 0), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_153 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 0) required_59), (placedSet 0 (1, 0) required_27)]
def childrenD_153 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 0) envelope_59), (placedSet 0 (1, 0) envelope_27)]
theorem common_sub_153 : commonEnvelope childrenD_153 ⊆ insert (0, 0) required_153 := by decide
theorem child_required_sub_153 : ∀ j, childrenC_153 j ⊆ insert (0, 0) required_153 := by decide
theorem child_envelope_sub_153 : ∀ j, childrenD_153 j ⊆ envelope_153 := by decide
theorem pivot_mem_153 : (0, 0) ∈ envelope_153 := by decide
theorem children_work_153 : ∀ j, Template HasSnaky 4 (childrenC_153 j) (childrenD_153 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_59 4 (-4, 0)).mono (by decide)
· exact (placed_template_map row_works_27 0 (1, 0)).mono (by decide)
theorem row_works_153 : Template HasSnaky 5 required_153 envelope_153 := by
refine compose HasSnaky 4 childrenC_153 childrenD_153 children_work_153 (0, 0)
required_153 envelope_153 pivot_mem_153 child_required_sub_153 child_envelope_sub_153 ?_
intro b hb; exact common_sub_153 (mem_commonEnvelope childrenD_153 b hb)
def required_155 : Finset Cell := ⟨(([(0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_155 : Finset Cell := ⟨(([(-1, -4), (-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_155 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 0) required_7), (placedSet 3 (0, 1) required_55)]
def childrenD_155 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 0) envelope_7), (placedSet 3 (0, 1) envelope_55)]
theorem common_sub_155 : commonEnvelope childrenD_155 ⊆ insert (0, 0) required_155 := by decide
theorem child_required_sub_155 : ∀ j, childrenC_155 j ⊆ insert (0, 0) required_155 := by decide
theorem child_envelope_sub_155 : ∀ j, childrenD_155 j ⊆ envelope_155 := by decide
theorem pivot_mem_155 : (0, 0) ∈ envelope_155 := by decide
theorem children_work_155 : ∀ j, Template HasSnaky 4 (childrenC_155 j) (childrenD_155 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_55 3 (0, 1)).mono (by decide)
theorem row_works_155 : Template HasSnaky 5 required_155 envelope_155 := by
refine compose HasSnaky 4 childrenC_155 childrenD_155 children_work_155 (0, 0)
required_155 envelope_155 pivot_mem_155 child_required_sub_155 child_envelope_sub_155 ?_
intro b hb; exact common_sub_155 (mem_commonEnvelope childrenD_155 b hb)
def required_157 : Finset Cell := ⟨(([(0, -1), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_157 : Finset Cell := ⟨(([(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_157 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 1 (1, 2) required_57)]
def childrenD_157 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 1 (1, 2) envelope_57)]
theorem common_sub_157 : commonEnvelope childrenD_157 ⊆ insert (0, 0) required_157 := by decide
theorem child_required_sub_157 : ∀ j, childrenC_157 j ⊆ insert (0, 0) required_157 := by decide
theorem child_envelope_sub_157 : ∀ j, childrenD_157 j ⊆ envelope_157 := by decide
theorem pivot_mem_157 : (0, 0) ∈ envelope_157 := by decide
theorem children_work_157 : ∀ j, Template HasSnaky 4 (childrenC_157 j) (childrenD_157 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_57 1 (1, 2)).mono (by decide)
theorem row_works_157 : Template HasSnaky 5 required_157 envelope_157 := by
refine compose HasSnaky 4 childrenC_157 childrenD_157 children_work_157 (0, 0)
required_157 envelope_157 pivot_mem_157 child_required_sub_157 child_envelope_sub_157 ?_
intro b hb; exact common_sub_157 (mem_commonEnvelope childrenD_157 b hb)
def required_158 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, -2), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_158 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, 0), (1, 1), (1, 2), (2, -1), (2, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_158 : Fin 3 → Finset Cell := ![(placedSet 0 (-1, 0) required_66), (placedSet 1 (0, 1) required_45), (placedSet 3 (0, 1) required_46)]
def childrenD_158 : Fin 3 → Finset Cell := ![(placedSet 0 (-1, 0) envelope_66), (placedSet 1 (0, 1) envelope_45), (placedSet 3 (0, 1) envelope_46)]
theorem common_sub_158 : commonEnvelope childrenD_158 ⊆ insert (0, 0) required_158 := by decide
theorem child_required_sub_158 : ∀ j, childrenC_158 j ⊆ insert (0, 0) required_158 := by decide
theorem child_envelope_sub_158 : ∀ j, childrenD_158 j ⊆ envelope_158 := by decide
theorem pivot_mem_158 : (0, 0) ∈ envelope_158 := by decide
theorem children_work_158 : ∀ j, Template HasSnaky 4 (childrenC_158 j) (childrenD_158 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_66 0 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_45 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_46 3 (0, 1)).mono (by decide)
theorem row_works_158 : Template HasSnaky 5 required_158 envelope_158 := by
refine compose HasSnaky 4 childrenC_158 childrenD_158 children_work_158 (0, 0)
required_158 envelope_158 pivot_mem_158 child_required_sub_158 child_envelope_sub_158 ?_
intro b hb; exact common_sub_158 (mem_commonEnvelope childrenD_158 b hb)
def required_163 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_163 : Finset Cell := ⟨(([(-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_163 : Fin 3 → Finset Cell := ![(placedSet 2 (1, 0) required_44), (placedSet 1 (1, 0) required_49), (placedSet 4 (-4, 0) required_56)]
def childrenD_163 : Fin 3 → Finset Cell := ![(placedSet 2 (1, 0) envelope_44), (placedSet 1 (1, 0) envelope_49), (placedSet 4 (-4, 0) envelope_56)]
theorem common_sub_163 : commonEnvelope childrenD_163 ⊆ insert (0, 0) required_163 := by decide
theorem child_required_sub_163 : ∀ j, childrenC_163 j ⊆ insert (0, 0) required_163 := by decide
theorem child_envelope_sub_163 : ∀ j, childrenD_163 j ⊆ envelope_163 := by decide
theorem pivot_mem_163 : (0, 0) ∈ envelope_163 := by decide
theorem children_work_163 : ∀ j, Template HasSnaky 4 (childrenC_163 j) (childrenD_163 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_44 2 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_49 1 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_56 4 (-4, 0)).mono (by decide)
theorem row_works_163 : Template HasSnaky 5 required_163 envelope_163 := by
refine compose HasSnaky 4 childrenC_163 childrenD_163 children_work_163 (0, 0)
required_163 envelope_163 pivot_mem_163 child_required_sub_163 child_envelope_sub_163 ?_
intro b hb; exact common_sub_163 (mem_commonEnvelope childrenD_163 b hb)
end SnakyConditional
end OAI
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