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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.Level06Part04
import OAI.GameTheory.SnakyConditional.Templates.Level06Part07
namespace OAI
namespace SnakyConditional
def required_167 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_167 : Finset Cell := ⟨(([(-5, 0), (-5, 1), (-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_167 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) required_57), (placedSet 4 (-4, 0) required_57)]
def childrenD_167 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) envelope_57), (placedSet 4 (-4, 0) envelope_57)]
theorem common_sub_167 : commonEnvelope childrenD_167 ⊆ insert (0, 0) required_167 := by decide
theorem child_required_sub_167 : ∀ j, childrenC_167 j ⊆ insert (0, 0) required_167 := by decide
theorem child_envelope_sub_167 : ∀ j, childrenD_167 j ⊆ envelope_167 := by decide
theorem pivot_mem_167 : (0, 0) ∈ envelope_167 := by decide
theorem children_work_167 : ∀ j, Template HasSnaky 4 (childrenC_167 j) (childrenD_167 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_57 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_57 4 (-4, 0)).mono (by decide)
theorem row_works_167 : Template HasSnaky 5 required_167 envelope_167 := by
refine compose HasSnaky 4 childrenC_167 childrenD_167 children_work_167 (0, 0)
required_167 envelope_167 pivot_mem_167 child_required_sub_167 child_envelope_sub_167 ?_
intro b hb; exact common_sub_167 (mem_commonEnvelope childrenD_167 b hb)
def required_181 : Finset Cell := ⟨(([(1, -2), (1, -1), (1, 0), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_181 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (0, 0), (0, 1), (0, 2), (0, 3), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1), (4, 1), (5, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_181 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) required_24), (placedSet 2 (2, 0) required_87), (placedSet 0 (3, 1) required_90)]
def childrenD_181 : Fin 3 → Finset Cell := ![(placedSet 3 (0, 1) envelope_24), (placedSet 2 (2, 0) envelope_87), (placedSet 0 (3, 1) envelope_90)]
theorem common_sub_181 : commonEnvelope childrenD_181 ⊆ insert (0, 0) required_181 := by decide
theorem child_required_sub_181 : ∀ j, childrenC_181 j ⊆ insert (0, 0) required_181 := by decide
theorem child_envelope_sub_181 : ∀ j, childrenD_181 j ⊆ envelope_181 := by decide
theorem pivot_mem_181 : (0, 0) ∈ envelope_181 := by decide
theorem children_work_181 : ∀ j, Template HasSnaky 4 (childrenC_181 j) (childrenD_181 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_24 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_87 2 (2, 0)).mono (by decide)
· exact (placed_template_map row_works_90 0 (3, 1)).mono (by decide)
theorem row_works_181 : Template HasSnaky 5 required_181 envelope_181 := by
refine compose HasSnaky 4 childrenC_181 childrenD_181 children_work_181 (0, 0)
required_181 envelope_181 pivot_mem_181 child_required_sub_181 child_envelope_sub_181 ?_
intro b hb; exact common_sub_181 (mem_commonEnvelope childrenD_181 b hb)
def required_182 : Finset Cell := ⟨(([(1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (3, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_182 : Finset Cell := ⟨(([(-1, 0), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (3, -1), (3, 0), (3, 1), (3, 2), (3, 3), (4, -1), (4, 0), (4, 1), (5, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_182 : Fin 2 → Finset Cell := ![(placedSet 2 (3, -1) required_12), (placedSet 0 (3, 0) required_139)]
def childrenD_182 : Fin 2 → Finset Cell := ![(placedSet 2 (3, -1) envelope_12), (placedSet 0 (3, 0) envelope_139)]
theorem common_sub_182 : commonEnvelope childrenD_182 ⊆ insert (0, 0) required_182 := by decide
theorem child_required_sub_182 : ∀ j, childrenC_182 j ⊆ insert (0, 0) required_182 := by decide
theorem child_envelope_sub_182 : ∀ j, childrenD_182 j ⊆ envelope_182 := by decide
theorem pivot_mem_182 : (0, 0) ∈ envelope_182 := by decide
theorem children_work_182 : ∀ j, Template HasSnaky 4 (childrenC_182 j) (childrenD_182 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_12 2 (3, -1)).mono (by decide)
· exact (placed_template_map row_works_139 0 (3, 0)).mono (by decide)
theorem row_works_182 : Template HasSnaky 5 required_182 envelope_182 := by
refine compose HasSnaky 4 childrenC_182 childrenD_182 children_work_182 (0, 0)
required_182 envelope_182 pivot_mem_182 child_required_sub_182 child_envelope_sub_182 ?_
intro b hb; exact common_sub_182 (mem_commonEnvelope childrenD_182 b hb)
def required_186 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_186 : Finset Cell := ⟨(([(-5, -1), (-5, 0), (-4, -1), (-4, 0), (-3, -1), (-3, 0), (-3, 1), (-2, 0), (-2, 1), (-1, 0), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_186 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) required_7), (placedSet 2 (1, 0) required_141)]
def childrenD_186 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) envelope_7), (placedSet 2 (1, 0) envelope_141)]
theorem common_sub_186 : commonEnvelope childrenD_186 ⊆ insert (0, 0) required_186 := by decide
theorem child_required_sub_186 : ∀ j, childrenC_186 j ⊆ insert (0, 0) required_186 := by decide
theorem child_envelope_sub_186 : ∀ j, childrenD_186 j ⊆ envelope_186 := by decide
theorem pivot_mem_186 : (0, 0) ∈ envelope_186 := by decide
theorem children_work_186 : ∀ j, Template HasSnaky 4 (childrenC_186 j) (childrenD_186 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 6 (-4, -1)).mono (by decide)
· exact (placed_template_map row_works_141 2 (1, 0)).mono (by decide)
theorem row_works_186 : Template HasSnaky 5 required_186 envelope_186 := by
refine compose HasSnaky 4 childrenC_186 childrenD_186 children_work_186 (0, 0)
required_186 envelope_186 pivot_mem_186 child_required_sub_186 child_envelope_sub_186 ?_
intro b hb; exact common_sub_186 (mem_commonEnvelope childrenD_186 b hb)
def required_194 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (-1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_194 : Finset Cell := ⟨(([(-4, -1), (-4, 1), (-3, -1), (-3, 1), (-2, -1), (-2, 1), (-2, 2), (-2, 3), (-2, 4), (-1, -2), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, 0), (0, 1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_194 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) required_0), (placedSet 4 (-2, 1) required_146)]
def childrenD_194 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) envelope_0), (placedSet 4 (-2, 1) envelope_146)]
theorem common_sub_194 : commonEnvelope childrenD_194 ⊆ insert (0, 0) required_194 := by decide
theorem child_required_sub_194 : ∀ j, childrenC_194 j ⊆ insert (0, 0) required_194 := by decide
theorem child_envelope_sub_194 : ∀ j, childrenD_194 j ⊆ envelope_194 := by decide
theorem pivot_mem_194 : (0, 0) ∈ envelope_194 := by decide
theorem children_work_194 : ∀ j, Template HasSnaky 4 (childrenC_194 j) (childrenD_194 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 0 (-4, -1)).mono (by decide)
· exact (placed_template_map row_works_146 4 (-2, 1)).mono (by decide)
theorem row_works_194 : Template HasSnaky 5 required_194 envelope_194 := by
refine compose HasSnaky 4 childrenC_194 childrenD_194 children_work_194 (0, 0)
required_194 envelope_194 pivot_mem_194 child_required_sub_194 child_envelope_sub_194 ?_
intro b hb; exact common_sub_194 (mem_commonEnvelope childrenD_194 b hb)
def required_201 : Finset Cell := ⟨(([(1, -2), (1, -1), (1, 0), (1, 1), (1, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_201 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (0, -1), (0, 0), (0, 2), (0, 3), (0, 4), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_201 : Fin 2 → Finset Cell := ![(placedSet 3 (1, 3) required_45), (placedSet 0 (2, 1) required_82)]
def childrenD_201 : Fin 2 → Finset Cell := ![(placedSet 3 (1, 3) envelope_45), (placedSet 0 (2, 1) envelope_82)]
theorem common_sub_201 : commonEnvelope childrenD_201 ⊆ insert (0, 0) required_201 := by decide
theorem child_required_sub_201 : ∀ j, childrenC_201 j ⊆ insert (0, 0) required_201 := by decide
theorem child_envelope_sub_201 : ∀ j, childrenD_201 j ⊆ envelope_201 := by decide
theorem pivot_mem_201 : (0, 0) ∈ envelope_201 := by decide
theorem children_work_201 : ∀ j, Template HasSnaky 4 (childrenC_201 j) (childrenD_201 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_45 3 (1, 3)).mono (by decide)
· exact (placed_template_map row_works_82 0 (2, 1)).mono (by decide)
theorem row_works_201 : Template HasSnaky 5 required_201 envelope_201 := by
refine compose HasSnaky 4 childrenC_201 childrenD_201 children_work_201 (0, 0)
required_201 envelope_201 pivot_mem_201 child_required_sub_201 child_envelope_sub_201 ?_
intro b hb; exact common_sub_201 (mem_commonEnvelope childrenD_201 b hb)
def required_209 : Finset Cell := ⟨(([(-3, 2), (-2, -1), (-2, 2), (-1, -1), (-1, 2), (0, -1), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_209 : Finset Cell := ⟨(([(-3, -1), (-3, 2), (-2, -1), (-2, 2), (-1, -1), (-1, 0), (-1, 2), (0, -1), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 2), (1, 3), (2, 0), (2, 3), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_209 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) required_25), (placedSet 5 (1, 3) required_81)]
def childrenD_209 : Fin 2 → Finset Cell := ![(placedSet 0 (1, 0) envelope_25), (placedSet 5 (1, 3) envelope_81)]
theorem common_sub_209 : commonEnvelope childrenD_209 ⊆ insert (0, 0) required_209 := by decide
theorem child_required_sub_209 : ∀ j, childrenC_209 j ⊆ insert (0, 0) required_209 := by decide
theorem child_envelope_sub_209 : ∀ j, childrenD_209 j ⊆ envelope_209 := by decide
theorem pivot_mem_209 : (0, 0) ∈ envelope_209 := by decide
theorem children_work_209 : ∀ j, Template HasSnaky 4 (childrenC_209 j) (childrenD_209 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_25 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_81 5 (1, 3)).mono (by decide)
theorem row_works_209 : Template HasSnaky 5 required_209 envelope_209 := by
refine compose HasSnaky 4 childrenC_209 childrenD_209 children_work_209 (0, 0)
required_209 envelope_209 pivot_mem_209 child_required_sub_209 child_envelope_sub_209 ?_
intro b hb; exact common_sub_209 (mem_commonEnvelope childrenD_209 b hb)
end SnakyConditional
end OAI
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