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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 | import OAI.GameTheory.SnakyConditional.Templates.Level05Part01
import OAI.GameTheory.SnakyConditional.Templates.Level05Part03
namespace OAI
namespace SnakyConditional
def required_44 : Finset Cell := ⟨(([(-4, 0), (-4, 1), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_44 : Finset Cell := ⟨(([(-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, 0), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_44 : Fin 2 → Finset Cell := ![(placedSet 4 (-3, 1) required_4), (placedSet 0 (0, 1) required_7)]
def childrenD_44 : Fin 2 → Finset Cell := ![(placedSet 4 (-3, 1) envelope_4), (placedSet 0 (0, 1) envelope_7)]
theorem common_sub_44 : commonEnvelope childrenD_44 ⊆ insert (0, 0) required_44 := by decide
theorem child_required_sub_44 : ∀ j, childrenC_44 j ⊆ insert (0, 0) required_44 := by decide
theorem child_envelope_sub_44 : ∀ j, childrenD_44 j ⊆ envelope_44 := by decide
theorem pivot_mem_44 : (0, 0) ∈ envelope_44 := by decide
theorem children_work_44 : ∀ j, Template HasSnaky 3 (childrenC_44 j) (childrenD_44 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 4 (-3, 1)).mono (by decide)
· exact (placed_template_map row_works_7 0 (0, 1)).mono (by decide)
theorem row_works_44 : Template HasSnaky 4 required_44 envelope_44 := by
refine compose HasSnaky 3 childrenC_44 childrenD_44 children_work_44 (0, 0)
required_44 envelope_44 pivot_mem_44 child_required_sub_44 child_envelope_sub_44 ?_
intro b hb; exact common_sub_44 (mem_commonEnvelope childrenD_44 b hb)
def required_45 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-3, 1), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_45 : Finset Cell := ⟨(([(-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, 0), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_45 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) required_6), (placedSet 0 (0, 1) required_7)]
def childrenD_45 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) envelope_6), (placedSet 0 (0, 1) envelope_7)]
theorem common_sub_45 : commonEnvelope childrenD_45 ⊆ insert (0, 0) required_45 := by decide
theorem child_required_sub_45 : ∀ j, childrenC_45 j ⊆ insert (0, 0) required_45 := by decide
theorem child_envelope_sub_45 : ∀ j, childrenD_45 j ⊆ envelope_45 := by decide
theorem pivot_mem_45 : (0, 0) ∈ envelope_45 := by decide
theorem children_work_45 : ∀ j, Template HasSnaky 3 (childrenC_45 j) (childrenD_45 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 4 (-4, 1)).mono (by decide)
· exact (placed_template_map row_works_7 0 (0, 1)).mono (by decide)
theorem row_works_45 : Template HasSnaky 4 required_45 envelope_45 := by
refine compose HasSnaky 3 childrenC_45 childrenD_45 children_work_45 (0, 0)
required_45 envelope_45 pivot_mem_45 child_required_sub_45 child_envelope_sub_45 ?_
intro b hb; exact common_sub_45 (mem_commonEnvelope childrenD_45 b hb)
def required_46 : Finset Cell := ⟨(([(-4, 0), (-3, -1), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_46 : Finset Cell := ⟨(([(-4, -1), (-4, 0), (-3, -1), (-3, 0), (-2, 0), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_46 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) required_6), (placedSet 0 (0, 1) required_7)]
def childrenD_46 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) envelope_6), (placedSet 0 (0, 1) envelope_7)]
theorem common_sub_46 : commonEnvelope childrenD_46 ⊆ insert (0, 0) required_46 := by decide
theorem child_required_sub_46 : ∀ j, childrenC_46 j ⊆ insert (0, 0) required_46 := by decide
theorem child_envelope_sub_46 : ∀ j, childrenD_46 j ⊆ envelope_46 := by decide
theorem pivot_mem_46 : (0, 0) ∈ envelope_46 := by decide
theorem children_work_46 : ∀ j, Template HasSnaky 3 (childrenC_46 j) (childrenD_46 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 6 (-4, -1)).mono (by decide)
· exact (placed_template_map row_works_7 0 (0, 1)).mono (by decide)
theorem row_works_46 : Template HasSnaky 4 required_46 envelope_46 := by
refine compose HasSnaky 3 childrenC_46 childrenD_46 children_work_46 (0, 0)
required_46 envelope_46 pivot_mem_46 child_required_sub_46 child_envelope_sub_46 ?_
intro b hb; exact common_sub_46 (mem_commonEnvelope childrenD_46 b hb)
def required_49 : Finset Cell := ⟨(([(-1, -4), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_49 : Finset Cell := ⟨(([(-1, -4), (-1, -3), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_49 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -3) required_4), (placedSet 1 (1, 0) required_7)]
def childrenD_49 : Fin 2 → Finset Cell := ![(placedSet 7 (-1, -3) envelope_4), (placedSet 1 (1, 0) envelope_7)]
theorem common_sub_49 : commonEnvelope childrenD_49 ⊆ insert (0, 0) required_49 := by decide
theorem child_required_sub_49 : ∀ j, childrenC_49 j ⊆ insert (0, 0) required_49 := by decide
theorem child_envelope_sub_49 : ∀ j, childrenD_49 j ⊆ envelope_49 := by decide
theorem pivot_mem_49 : (0, 0) ∈ envelope_49 := by decide
theorem children_work_49 : ∀ j, Template HasSnaky 3 (childrenC_49 j) (childrenD_49 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 7 (-1, -3)).mono (by decide)
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
theorem row_works_49 : Template HasSnaky 4 required_49 envelope_49 := by
refine compose HasSnaky 3 childrenC_49 childrenD_49 children_work_49 (0, 0)
required_49 envelope_49 pivot_mem_49 child_required_sub_49 child_envelope_sub_49 ?_
intro b hb; exact common_sub_49 (mem_commonEnvelope childrenD_49 b hb)
def required_50 : Finset Cell := ⟨(([(-1, 0), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_50 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_50 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, 1) required_6), (placedSet 1 (1, 0) required_7)]
def childrenD_50 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, 1) envelope_6), (placedSet 1 (1, 0) envelope_7)]
theorem common_sub_50 : commonEnvelope childrenD_50 ⊆ insert (0, 0) required_50 := by decide
theorem child_required_sub_50 : ∀ j, childrenC_50 j ⊆ insert (0, 0) required_50 := by decide
theorem child_envelope_sub_50 : ∀ j, childrenD_50 j ⊆ envelope_50 := by decide
theorem pivot_mem_50 : (0, 0) ∈ envelope_50 := by decide
theorem children_work_50 : ∀ j, Template HasSnaky 3 (childrenC_50 j) (childrenD_50 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 3 (-1, 1)).mono (by decide)
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
theorem row_works_50 : Template HasSnaky 4 required_50 envelope_50 := by
refine compose HasSnaky 3 childrenC_50 childrenD_50 children_work_50 (0, 0)
required_50 envelope_50 pivot_mem_50 child_required_sub_50 child_envelope_sub_50 ?_
intro b hb; exact common_sub_50 (mem_commonEnvelope childrenD_50 b hb)
def required_51 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-2, -1), (-2, 0), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_51 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_51 : Fin 4 → Finset Cell := ![(placedSet 2 (1, -1) required_10), (placedSet 0 (1, 0) required_10), (placedSet 2 (-1, 0) required_26), (placedSet 0 (-1, -1) required_26)]
def childrenD_51 : Fin 4 → Finset Cell := ![(placedSet 2 (1, -1) envelope_10), (placedSet 0 (1, 0) envelope_10), (placedSet 2 (-1, 0) envelope_26), (placedSet 0 (-1, -1) envelope_26)]
theorem common_sub_51 : commonEnvelope childrenD_51 ⊆ insert (0, 0) required_51 := by decide
theorem child_required_sub_51 : ∀ j, childrenC_51 j ⊆ insert (0, 0) required_51 := by decide
theorem child_envelope_sub_51 : ∀ j, childrenD_51 j ⊆ envelope_51 := by decide
theorem pivot_mem_51 : (0, 0) ∈ envelope_51 := by decide
theorem children_work_51 : ∀ j, Template HasSnaky 3 (childrenC_51 j) (childrenD_51 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_10 2 (1, -1)).mono (by decide)
· exact (placed_template_map row_works_10 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_26 2 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_26 0 (-1, -1)).mono (by decide)
theorem row_works_51 : Template HasSnaky 4 required_51 envelope_51 := by
refine compose HasSnaky 3 childrenC_51 childrenD_51 children_work_51 (0, 0)
required_51 envelope_51 pivot_mem_51 child_required_sub_51 child_envelope_sub_51 ?_
intro b hb; exact common_sub_51 (mem_commonEnvelope childrenD_51 b hb)
def required_55 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_55 : Finset Cell := ⟨(([(-5, 1), (-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, 0), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_55 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) required_7), (placedSet 0 (0, 1) required_7)]
def childrenD_55 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) envelope_7), (placedSet 0 (0, 1) envelope_7)]
theorem common_sub_55 : commonEnvelope childrenD_55 ⊆ insert (0, 0) required_55 := by decide
theorem child_required_sub_55 : ∀ j, childrenC_55 j ⊆ insert (0, 0) required_55 := by decide
theorem child_envelope_sub_55 : ∀ j, childrenD_55 j ⊆ envelope_55 := by decide
theorem pivot_mem_55 : (0, 0) ∈ envelope_55 := by decide
theorem children_work_55 : ∀ j, Template HasSnaky 3 (childrenC_55 j) (childrenD_55 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_7 4 (-4, 1)).mono (by decide)
· exact (placed_template_map row_works_7 0 (0, 1)).mono (by decide)
theorem row_works_55 : Template HasSnaky 4 required_55 envelope_55 := by
refine compose HasSnaky 3 childrenC_55 childrenD_55 children_work_55 (0, 0)
required_55 envelope_55 pivot_mem_55 child_required_sub_55 child_envelope_sub_55 ?_
intro b hb; exact common_sub_55 (mem_commonEnvelope childrenD_55 b hb)
end SnakyConditional
end OAI
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