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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part06
import OAI.GameTheory.SnakyConditional.Templates.Level07Part01
import OAI.GameTheory.SnakyConditional.Templates.Level07Part02
import OAI.GameTheory.SnakyConditional.Templates.Level07Part03
import OAI.GameTheory.SnakyConditional.Templates.Level07Part05
import OAI.GameTheory.SnakyConditional.Templates.Level07Part06
namespace OAI
namespace SnakyConditional
def required_180 : Finset Cell := ⟨(([(0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_180 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_180 : Fin 4 → Finset Cell := ![(placedSet 3 (-1, 0) required_7), (placedSet 0 (-1, 1) required_63), (placedSet 0 (0, 1) required_155), (placedSet 0 (-1, -1) required_132)]
def childrenD_180 : Fin 4 → Finset Cell := ![(placedSet 3 (-1, 0) envelope_7), (placedSet 0 (-1, 1) envelope_63), (placedSet 0 (0, 1) envelope_155), (placedSet 0 (-1, -1) envelope_132)]
theorem common_sub_180 : commonEnvelope childrenD_180 ⊆ insert (0, 0) required_180 := by decide
theorem child_required_sub_180 : ∀ j, childrenC_180 j ⊆ insert (0, 0) required_180 := by decide
theorem child_envelope_sub_180 : ∀ j, childrenD_180 j ⊆ envelope_180 := by decide
theorem pivot_mem_180 : (0, 0) ∈ envelope_180 := by decide
theorem children_work_180 : ∀ j, Template HasSnaky 5 (childrenC_180 j) (childrenD_180 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 3 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_63 0 (-1, 1)).mono (by decide)
· exact (placed_template_map row_works_155 0 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_132 0 (-1, -1)).mono (by decide)
theorem row_works_180 : Template HasSnaky 6 required_180 envelope_180 := by
refine compose HasSnaky 5 childrenC_180 childrenD_180 children_work_180 (0, 0)
required_180 envelope_180 pivot_mem_180 child_required_sub_180 child_envelope_sub_180 ?_
intro b hb; exact common_sub_180 (mem_commonEnvelope childrenD_180 b hb)
def required_183 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_183 : Finset Cell := ⟨(([(-5, -1), (-5, 1), (-4, -1), (-4, 0), (-4, 1), (-3, -1), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-2, 1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_183 : Fin 3 → Finset Cell := ![(placedSet 2 (-3, 1) required_64), (placedSet 3 (-4, -1) required_63), (placedSet 2 (1, 0) required_55)]
def childrenD_183 : Fin 3 → Finset Cell := ![(placedSet 2 (-3, 1) envelope_64), (placedSet 3 (-4, -1) envelope_63), (placedSet 2 (1, 0) envelope_55)]
theorem common_sub_183 : commonEnvelope childrenD_183 ⊆ insert (0, 0) required_183 := by decide
theorem child_required_sub_183 : ∀ j, childrenC_183 j ⊆ insert (0, 0) required_183 := by decide
theorem child_envelope_sub_183 : ∀ j, childrenD_183 j ⊆ envelope_183 := by decide
theorem pivot_mem_183 : (0, 0) ∈ envelope_183 := by decide
theorem children_work_183 : ∀ j, Template HasSnaky 5 (childrenC_183 j) (childrenD_183 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_64 2 (-3, 1)).mono (by decide)
· exact (placed_template_map row_works_63 3 (-4, -1)).mono (by decide)
· exact (placed_template_map row_works_55 2 (1, 0)).mono (by decide)
theorem row_works_183 : Template HasSnaky 6 required_183 envelope_183 := by
refine compose HasSnaky 5 childrenC_183 childrenD_183 children_work_183 (0, 0)
required_183 envelope_183 pivot_mem_183 child_required_sub_183 child_envelope_sub_183 ?_
intro b hb; exact common_sub_183 (mem_commonEnvelope childrenD_183 b hb)
def required_185 : Finset Cell := ⟨(([(-1, -3), (-1, -1), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_185 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_185 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) required_44), (placedSet 0 (0, 1) required_49), (placedSet 0 (-1, 0) required_84)]
def childrenD_185 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) envelope_44), (placedSet 0 (0, 1) envelope_49), (placedSet 0 (-1, 0) envelope_84)]
theorem common_sub_185 : commonEnvelope childrenD_185 ⊆ insert (0, 0) required_185 := by decide
theorem child_required_sub_185 : ∀ j, childrenC_185 j ⊆ insert (0, 0) required_185 := by decide
theorem child_envelope_sub_185 : ∀ j, childrenD_185 j ⊆ envelope_185 := by decide
theorem pivot_mem_185 : (0, 0) ∈ envelope_185 := by decide
theorem children_work_185 : ∀ j, Template HasSnaky 5 (childrenC_185 j) (childrenD_185 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_44 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_49 0 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_84 0 (-1, 0)).mono (by decide)
theorem row_works_185 : Template HasSnaky 6 required_185 envelope_185 := by
refine compose HasSnaky 5 childrenC_185 childrenD_185 children_work_185 (0, 0)
required_185 envelope_185 pivot_mem_185 child_required_sub_185 child_envelope_sub_185 ?_
intro b hb; exact common_sub_185 (mem_commonEnvelope childrenD_185 b hb)
def required_188 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (2, 0), (3, -2), (4, -2), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_188 : Finset Cell := ⟨(([(0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, 0), (3, -3), (3, -2), (3, -1), (3, 0), (3, 1), (4, -2), (4, -1), (4, 0), (4, 1), (5, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_188 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 5 (3, 0) required_112)]
def childrenD_188 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 5 (3, 0) envelope_112)]
theorem common_sub_188 : commonEnvelope childrenD_188 ⊆ insert (0, 0) required_188 := by decide
theorem child_required_sub_188 : ∀ j, childrenC_188 j ⊆ insert (0, 0) required_188 := by decide
theorem child_envelope_sub_188 : ∀ j, childrenD_188 j ⊆ envelope_188 := by decide
theorem pivot_mem_188 : (0, 0) ∈ envelope_188 := by decide
theorem children_work_188 : ∀ j, Template HasSnaky 5 (childrenC_188 j) (childrenD_188 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_112 5 (3, 0)).mono (by decide)
theorem row_works_188 : Template HasSnaky 6 required_188 envelope_188 := by
refine compose HasSnaky 5 childrenC_188 childrenD_188 children_work_188 (0, 0)
required_188 envelope_188 pivot_mem_188 child_required_sub_188 child_envelope_sub_188 ?_
intro b hb; exact common_sub_188 (mem_commonEnvelope childrenD_188 b hb)
def required_189 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_189 : Finset Cell := ⟨(([(-4, 0), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, -2), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_189 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) required_12), (placedSet 4 (-3, 0) required_86)]
def childrenD_189 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) envelope_12), (placedSet 4 (-3, 0) envelope_86)]
theorem common_sub_189 : commonEnvelope childrenD_189 ⊆ insert (0, 0) required_189 := by decide
theorem child_required_sub_189 : ∀ j, childrenC_189 j ⊆ insert (0, 0) required_189 := by decide
theorem child_envelope_sub_189 : ∀ j, childrenD_189 j ⊆ envelope_189 := by decide
theorem pivot_mem_189 : (0, 0) ∈ envelope_189 := by decide
theorem children_work_189 : ∀ j, Template HasSnaky 5 (childrenC_189 j) (childrenD_189 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_12 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_86 4 (-3, 0)).mono (by decide)
theorem row_works_189 : Template HasSnaky 6 required_189 envelope_189 := by
refine compose HasSnaky 5 childrenC_189 childrenD_189 children_work_189 (0, 0)
required_189 envelope_189 pivot_mem_189 child_required_sub_189 child_envelope_sub_189 ?_
intro b hb; exact common_sub_189 (mem_commonEnvelope childrenD_189 b hb)
def required_192 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_192 : Finset Cell := ⟨(([(-2, 0), (-1, -4), (-1, -3), (-1, -2), (-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (1, 2), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_192 : Fin 3 → Finset Cell := ![(placedSet 1 (-1, -3) required_64), (placedSet 0 (-1, 0) required_103), (placedSet 3 (0, 1) required_55)]
def childrenD_192 : Fin 3 → Finset Cell := ![(placedSet 1 (-1, -3) envelope_64), (placedSet 0 (-1, 0) envelope_103), (placedSet 3 (0, 1) envelope_55)]
theorem common_sub_192 : commonEnvelope childrenD_192 ⊆ insert (0, 0) required_192 := by decide
theorem child_required_sub_192 : ∀ j, childrenC_192 j ⊆ insert (0, 0) required_192 := by decide
theorem child_envelope_sub_192 : ∀ j, childrenD_192 j ⊆ envelope_192 := by decide
theorem pivot_mem_192 : (0, 0) ∈ envelope_192 := by decide
theorem children_work_192 : ∀ j, Template HasSnaky 5 (childrenC_192 j) (childrenD_192 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_64 1 (-1, -3)).mono (by decide)
· exact (placed_template_map row_works_103 0 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_55 3 (0, 1)).mono (by decide)
theorem row_works_192 : Template HasSnaky 6 required_192 envelope_192 := by
refine compose HasSnaky 5 childrenC_192 childrenD_192 children_work_192 (0, 0)
required_192 envelope_192 pivot_mem_192 child_required_sub_192 child_envelope_sub_192 ?_
intro b hb; exact common_sub_192 (mem_commonEnvelope childrenD_192 b hb)
def required_197 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_197 : Finset Cell := ⟨(([(-5, -1), (-5, 1), (-4, -1), (-4, 0), (-4, 1), (-3, -1), (-3, 0), (-3, 1), (-2, 0), (-1, 0), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_197 : Fin 2 → Finset Cell := ![(placedSet 3 (-4, -1) required_63), (placedSet 1 (1, -1) required_63)]
def childrenD_197 : Fin 2 → Finset Cell := ![(placedSet 3 (-4, -1) envelope_63), (placedSet 1 (1, -1) envelope_63)]
theorem common_sub_197 : commonEnvelope childrenD_197 ⊆ insert (0, 0) required_197 := by decide
theorem child_required_sub_197 : ∀ j, childrenC_197 j ⊆ insert (0, 0) required_197 := by decide
theorem child_envelope_sub_197 : ∀ j, childrenD_197 j ⊆ envelope_197 := by decide
theorem pivot_mem_197 : (0, 0) ∈ envelope_197 := by decide
theorem children_work_197 : ∀ j, Template HasSnaky 5 (childrenC_197 j) (childrenD_197 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_63 3 (-4, -1)).mono (by decide)
· exact (placed_template_map row_works_63 1 (1, -1)).mono (by decide)
theorem row_works_197 : Template HasSnaky 6 required_197 envelope_197 := by
refine compose HasSnaky 5 childrenC_197 childrenD_197 children_work_197 (0, 0)
required_197 envelope_197 pivot_mem_197 child_required_sub_197 child_envelope_sub_197 ?_
intro b hb; exact common_sub_197 (mem_commonEnvelope childrenD_197 b hb)
end SnakyConditional
end OAI
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