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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 | import OAI.GameTheory.SnakyConditional.Templates.Level07Part01
import OAI.GameTheory.SnakyConditional.Templates.Level07Part04
import OAI.GameTheory.SnakyConditional.Templates.Level07Part05
import OAI.GameTheory.SnakyConditional.Templates.Level07Part06
import OAI.GameTheory.SnakyConditional.Templates.Level07Part07
namespace OAI
namespace SnakyConditional
def required_216 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_216 : Finset Cell := ⟨(([(-5, -1), (-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), (1, 1), (2, -1), (2, 0), (2, 1), (3, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_216 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) required_7), (placedSet 5 (1, 0) required_155)]
def childrenD_216 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) envelope_7), (placedSet 5 (1, 0) envelope_155)]
theorem common_sub_216 : commonEnvelope childrenD_216 ⊆ insert (0, 0) required_216 := by decide
theorem child_required_sub_216 : ∀ j, childrenC_216 j ⊆ insert (0, 0) required_216 := by decide
theorem child_envelope_sub_216 : ∀ j, childrenD_216 j ⊆ envelope_216 := by decide
theorem pivot_mem_216 : (0, 0) ∈ envelope_216 := by decide
theorem children_work_216 : ∀ j, Template HasSnaky 5 (childrenC_216 j) (childrenD_216 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_155 5 (1, 0)).mono (by decide)
theorem row_works_216 : Template HasSnaky 6 required_216 envelope_216 := by
refine compose HasSnaky 5 childrenC_216 childrenD_216 children_work_216 (0, 0)
required_216 envelope_216 pivot_mem_216 child_required_sub_216 child_envelope_sub_216 ?_
intro b hb; exact common_sub_216 (mem_commonEnvelope childrenD_216 b hb)
def required_218 : Finset Cell := ⟨(([(-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -1), (1, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_218 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3), (2, -1), (2, 0), (2, 1), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_218 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) required_0), (placedSet 0 (-2, 0) required_182)]
def childrenD_218 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) envelope_0), (placedSet 0 (-2, 0) envelope_182)]
theorem common_sub_218 : commonEnvelope childrenD_218 ⊆ insert (0, 0) required_218 := by decide
theorem child_required_sub_218 : ∀ j, childrenC_218 j ⊆ insert (0, 0) required_218 := by decide
theorem child_envelope_sub_218 : ∀ j, childrenD_218 j ⊆ envelope_218 := by decide
theorem pivot_mem_218 : (0, 0) ∈ envelope_218 := by decide
theorem children_work_218 : ∀ j, Template HasSnaky 5 (childrenC_218 j) (childrenD_218 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_182 0 (-2, 0)).mono (by decide)
theorem row_works_218 : Template HasSnaky 6 required_218 envelope_218 := by
refine compose HasSnaky 5 childrenC_218 childrenD_218 children_work_218 (0, 0)
required_218 envelope_218 pivot_mem_218 child_required_sub_218 child_envelope_sub_218 ?_
intro b hb; exact common_sub_218 (mem_commonEnvelope childrenD_218 b hb)
def required_222 : Finset Cell := ⟨(([(-2, 0), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, -3), (0, -2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_222 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, -3), (0, -2), (0, 0), (0, 1), (1, -2), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1), (3, -1), (3, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_222 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 5 (1, 0) required_158)]
def childrenD_222 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 5 (1, 0) envelope_158)]
theorem common_sub_222 : commonEnvelope childrenD_222 ⊆ insert (0, 0) required_222 := by decide
theorem child_required_sub_222 : ∀ j, childrenC_222 j ⊆ insert (0, 0) required_222 := by decide
theorem child_envelope_sub_222 : ∀ j, childrenD_222 j ⊆ envelope_222 := by decide
theorem pivot_mem_222 : (0, 0) ∈ envelope_222 := by decide
theorem children_work_222 : ∀ j, Template HasSnaky 5 (childrenC_222 j) (childrenD_222 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_158 5 (1, 0)).mono (by decide)
theorem row_works_222 : Template HasSnaky 6 required_222 envelope_222 := by
refine compose HasSnaky 5 childrenC_222 childrenD_222 children_work_222 (0, 0)
required_222 envelope_222 pivot_mem_222 child_required_sub_222 child_envelope_sub_222 ?_
intro b hb; exact common_sub_222 (mem_commonEnvelope childrenD_222 b hb)
def required_228 : Finset Cell := ⟨(([(1, -2), (1, -1), (1, 0), (1, 1), (1, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_228 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (0, -1), (0, 0), (0, 1), (0, 3), (0, 4), (0, 5), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (3, 1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_228 : Fin 2 → Finset Cell := ![(placedSet 0 (2, 1) required_82), (placedSet 3 (1, 3) required_68)]
def childrenD_228 : Fin 2 → Finset Cell := ![(placedSet 0 (2, 1) envelope_82), (placedSet 3 (1, 3) envelope_68)]
theorem common_sub_228 : commonEnvelope childrenD_228 ⊆ insert (0, 0) required_228 := by decide
theorem child_required_sub_228 : ∀ j, childrenC_228 j ⊆ insert (0, 0) required_228 := by decide
theorem child_envelope_sub_228 : ∀ j, childrenD_228 j ⊆ envelope_228 := by decide
theorem pivot_mem_228 : (0, 0) ∈ envelope_228 := by decide
theorem children_work_228 : ∀ j, Template HasSnaky 5 (childrenC_228 j) (childrenD_228 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_82 0 (2, 1)).mono (by decide)
· exact (placed_template_map row_works_68 3 (1, 3)).mono (by decide)
theorem row_works_228 : Template HasSnaky 6 required_228 envelope_228 := by
refine compose HasSnaky 5 childrenC_228 childrenD_228 children_work_228 (0, 0)
required_228 envelope_228 pivot_mem_228 child_required_sub_228 child_envelope_sub_228 ?_
intro b hb; exact common_sub_228 (mem_commonEnvelope childrenD_228 b hb)
def required_233 : Finset Cell := ⟨(([(-1, -2), (0, -2), (0, -1), (1, -2), (2, -2), (2, -1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_233 : Finset Cell := ⟨(([(-2, -3), (-1, -3), (-1, -2), (-1, 0), (0, -2), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, 0), (2, -2), (2, -1), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 1), (5, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_233 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, -3) required_32), (placedSet 0 (2, 0) required_133)]
def childrenD_233 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, -3) envelope_32), (placedSet 0 (2, 0) envelope_133)]
theorem common_sub_233 : commonEnvelope childrenD_233 ⊆ insert (0, 0) required_233 := by decide
theorem child_required_sub_233 : ∀ j, childrenC_233 j ⊆ insert (0, 0) required_233 := by decide
theorem child_envelope_sub_233 : ∀ j, childrenD_233 j ⊆ envelope_233 := by decide
theorem pivot_mem_233 : (0, 0) ∈ envelope_233 := by decide
theorem children_work_233 : ∀ j, Template HasSnaky 5 (childrenC_233 j) (childrenD_233 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_32 3 (-1, -3)).mono (by decide)
· exact (placed_template_map row_works_133 0 (2, 0)).mono (by decide)
theorem row_works_233 : Template HasSnaky 6 required_233 envelope_233 := by
refine compose HasSnaky 5 childrenC_233 childrenD_233 children_work_233 (0, 0)
required_233 envelope_233 pivot_mem_233 child_required_sub_233 child_envelope_sub_233 ?_
intro b hb; exact common_sub_233 (mem_commonEnvelope childrenD_233 b hb)
def required_236 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_236 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-1, -4), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, -2), (0, -1), (0, 0), (0, 1), (0, 2), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_236 : Fin 4 → Finset Cell := ![(placedSet 1 (0, 1) required_38), (placedSet 7 (-1, 0) required_122), (placedSet 0 (-2, -1) required_181), (placedSet 1 (0, -1) required_30)]
def childrenD_236 : Fin 4 → Finset Cell := ![(placedSet 1 (0, 1) envelope_38), (placedSet 7 (-1, 0) envelope_122), (placedSet 0 (-2, -1) envelope_181), (placedSet 1 (0, -1) envelope_30)]
theorem common_sub_236 : commonEnvelope childrenD_236 ⊆ insert (0, 0) required_236 := by decide
theorem child_required_sub_236 : ∀ j, childrenC_236 j ⊆ insert (0, 0) required_236 := by decide
theorem child_envelope_sub_236 : ∀ j, childrenD_236 j ⊆ envelope_236 := by decide
theorem pivot_mem_236 : (0, 0) ∈ envelope_236 := by decide
theorem children_work_236 : ∀ j, Template HasSnaky 5 (childrenC_236 j) (childrenD_236 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_38 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_122 7 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_181 0 (-2, -1)).mono (by decide)
· exact (placed_template_map row_works_30 1 (0, -1)).mono (by decide)
theorem row_works_236 : Template HasSnaky 6 required_236 envelope_236 := by
refine compose HasSnaky 5 childrenC_236 childrenD_236 children_work_236 (0, 0)
required_236 envelope_236 pivot_mem_236 child_required_sub_236 child_envelope_sub_236 ?_
intro b hb; exact common_sub_236 (mem_commonEnvelope childrenD_236 b hb)
def required_270 : Finset Cell := ⟨(([(-1, -1), (0, -1), (0, 1), (0, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_270 : Finset Cell := ⟨(([(-1, -2), (-1, -1), (-1, 2), (-1, 3), (-1, 4), (0, -1), (0, 0), (0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (1, 4)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_270 : Fin 2 → Finset Cell := ![(placedSet 0 (-1, 3) required_63), (placedSet 7 (-1, -2) required_6)]
def childrenD_270 : Fin 2 → Finset Cell := ![(placedSet 0 (-1, 3) envelope_63), (placedSet 7 (-1, -2) envelope_6)]
theorem common_sub_270 : commonEnvelope childrenD_270 ⊆ insert (0, 0) required_270 := by decide
theorem child_required_sub_270 : ∀ j, childrenC_270 j ⊆ insert (0, 0) required_270 := by decide
theorem child_envelope_sub_270 : ∀ j, childrenD_270 j ⊆ envelope_270 := by decide
theorem pivot_mem_270 : (0, 0) ∈ envelope_270 := by decide
theorem children_work_270 : ∀ j, Template HasSnaky 5 (childrenC_270 j) (childrenD_270 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_63 0 (-1, 3)).mono (by decide)
· exact (placed_template_map row_works_6 7 (-1, -2)).mono (by decide)
theorem row_works_270 : Template HasSnaky 6 required_270 envelope_270 := by
refine compose HasSnaky 5 childrenC_270 childrenD_270 children_work_270 (0, 0)
required_270 envelope_270 pivot_mem_270 child_required_sub_270 child_envelope_sub_270 ?_
intro b hb; exact common_sub_270 (mem_commonEnvelope childrenD_270 b hb)
end SnakyConditional
end OAI
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