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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.Level05Part04
import OAI.GameTheory.SnakyConditional.Templates.Level05Part06
import OAI.GameTheory.SnakyConditional.Templates.Level05Part07
namespace OAI
namespace SnakyConditional
def required_69 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_69 : Finset Cell := ⟨(([(0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (2, 1), (2, 2), (3, 1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_69 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 0 (2, 1) required_34)]
def childrenD_69 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 0 (2, 1) envelope_34)]
theorem common_sub_69 : commonEnvelope childrenD_69 ⊆ insert (0, 0) required_69 := by decide
theorem child_required_sub_69 : ∀ j, childrenC_69 j ⊆ insert (0, 0) required_69 := by decide
theorem child_envelope_sub_69 : ∀ j, childrenD_69 j ⊆ envelope_69 := by decide
theorem pivot_mem_69 : (0, 0) ∈ envelope_69 := by decide
theorem children_work_69 : ∀ j, Template HasSnaky 3 (childrenC_69 j) (childrenD_69 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_34 0 (2, 1)).mono (by decide)
theorem row_works_69 : Template HasSnaky 4 required_69 envelope_69 := by
refine compose HasSnaky 3 childrenC_69 childrenD_69 children_work_69 (0, 0)
required_69 envelope_69 pivot_mem_69 child_required_sub_69 child_envelope_sub_69 ?_
intro b hb; exact common_sub_69 (mem_commonEnvelope childrenD_69 b hb)
def required_70 : Finset Cell := ⟨(([(1, -4), (1, -3), (1, -2), (1, -1), (2, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_70 : Finset Cell := ⟨(([(0, -1), (0, 0), (0, 1), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0), (2, -1), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_70 : Fin 2 → Finset Cell := ![(placedSet 3 (0, -1) required_4), (placedSet 0 (1, 0) required_41)]
def childrenD_70 : Fin 2 → Finset Cell := ![(placedSet 3 (0, -1) envelope_4), (placedSet 0 (1, 0) envelope_41)]
theorem common_sub_70 : commonEnvelope childrenD_70 ⊆ insert (0, 0) required_70 := by decide
theorem child_required_sub_70 : ∀ j, childrenC_70 j ⊆ insert (0, 0) required_70 := by decide
theorem child_envelope_sub_70 : ∀ j, childrenD_70 j ⊆ envelope_70 := by decide
theorem pivot_mem_70 : (0, 0) ∈ envelope_70 := by decide
theorem children_work_70 : ∀ j, Template HasSnaky 3 (childrenC_70 j) (childrenD_70 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_4 3 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_41 0 (1, 0)).mono (by decide)
theorem row_works_70 : Template HasSnaky 4 required_70 envelope_70 := by
refine compose HasSnaky 3 childrenC_70 childrenD_70 children_work_70 (0, 0)
required_70 envelope_70 pivot_mem_70 child_required_sub_70 child_envelope_sub_70 ?_
intro b hb; exact common_sub_70 (mem_commonEnvelope childrenD_70 b hb)
def required_72 : Finset Cell := ⟨(([(-2, 1), (-1, 1), (-1, 2), (-1, 3), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_72 : Finset Cell := ⟨(([(-3, 1), (-2, 1), (-1, 1), (-1, 2), (-1, 3), (-1, 4), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_72 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 4) required_0), (placedSet 6 (1, 0) required_8)]
def childrenD_72 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 4) envelope_0), (placedSet 6 (1, 0) envelope_8)]
theorem common_sub_72 : commonEnvelope childrenD_72 ⊆ insert (0, 0) required_72 := by decide
theorem child_required_sub_72 : ∀ j, childrenC_72 j ⊆ insert (0, 0) required_72 := by decide
theorem child_envelope_sub_72 : ∀ j, childrenD_72 j ⊆ envelope_72 := by decide
theorem pivot_mem_72 : (0, 0) ∈ envelope_72 := by decide
theorem children_work_72 : ∀ j, Template HasSnaky 3 (childrenC_72 j) (childrenD_72 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 5 (-1, 4)).mono (by decide)
· exact (placed_template_map row_works_8 6 (1, 0)).mono (by decide)
theorem row_works_72 : Template HasSnaky 4 required_72 envelope_72 := by
refine compose HasSnaky 3 childrenC_72 childrenD_72 children_work_72 (0, 0)
required_72 envelope_72 pivot_mem_72 child_required_sub_72 child_envelope_sub_72 ?_
intro b hb; exact common_sub_72 (mem_commonEnvelope childrenD_72 b hb)
def required_74 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (0, -2), (0, 1), (1, -2), (2, -2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_74 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, -2), (0, -1), (0, 0), (0, 1), (1, -2), (2, -2)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_74 : Fin 2 → Finset Cell := ![(placedSet 7 (0, -1) required_2), (placedSet 0 (-1, -1) required_53)]
def childrenD_74 : Fin 2 → Finset Cell := ![(placedSet 7 (0, -1) envelope_2), (placedSet 0 (-1, -1) envelope_53)]
theorem common_sub_74 : commonEnvelope childrenD_74 ⊆ insert (0, 0) required_74 := by decide
theorem child_required_sub_74 : ∀ j, childrenC_74 j ⊆ insert (0, 0) required_74 := by decide
theorem child_envelope_sub_74 : ∀ j, childrenD_74 j ⊆ envelope_74 := by decide
theorem pivot_mem_74 : (0, 0) ∈ envelope_74 := by decide
theorem children_work_74 : ∀ j, Template HasSnaky 3 (childrenC_74 j) (childrenD_74 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_2 7 (0, -1)).mono (by decide)
· exact (placed_template_map row_works_53 0 (-1, -1)).mono (by decide)
theorem row_works_74 : Template HasSnaky 4 required_74 envelope_74 := by
refine compose HasSnaky 3 childrenC_74 childrenD_74 children_work_74 (0, 0)
required_74 envelope_74 pivot_mem_74 child_required_sub_74 child_envelope_sub_74 ?_
intro b hb; exact common_sub_74 (mem_commonEnvelope childrenD_74 b hb)
def required_75 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (0, -1), (1, -1), (1, 0), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_75 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_75 : Fin 2 → Finset Cell := ![(placedSet 0 (-3, -1) required_0), (placedSet 0 (3, -1) required_9)]
def childrenD_75 : Fin 2 → Finset Cell := ![(placedSet 0 (-3, -1) envelope_0), (placedSet 0 (3, -1) envelope_9)]
theorem common_sub_75 : commonEnvelope childrenD_75 ⊆ insert (0, 0) required_75 := by decide
theorem child_required_sub_75 : ∀ j, childrenC_75 j ⊆ insert (0, 0) required_75 := by decide
theorem child_envelope_sub_75 : ∀ j, childrenD_75 j ⊆ envelope_75 := by decide
theorem pivot_mem_75 : (0, 0) ∈ envelope_75 := by decide
theorem children_work_75 : ∀ j, Template HasSnaky 3 (childrenC_75 j) (childrenD_75 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 0 (-3, -1)).mono (by decide)
· exact (placed_template_map row_works_9 0 (3, -1)).mono (by decide)
theorem row_works_75 : Template HasSnaky 4 required_75 envelope_75 := by
refine compose HasSnaky 3 childrenC_75 childrenD_75 children_work_75 (0, 0)
required_75 envelope_75 pivot_mem_75 child_required_sub_75 child_envelope_sub_75 ?_
intro b hb; exact common_sub_75 (mem_commonEnvelope childrenD_75 b hb)
def required_79 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, 0), (2, -1), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_79 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (0, -3), (0, -2), (0, -1), (0, 0), (1, 0), (1, 1), (2, -1), (2, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_79 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 1) required_6), (placedSet 0 (-1, 0) required_48)]
def childrenD_79 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 1) envelope_6), (placedSet 0 (-1, 0) envelope_48)]
theorem common_sub_79 : commonEnvelope childrenD_79 ⊆ insert (0, 0) required_79 := by decide
theorem child_required_sub_79 : ∀ j, childrenC_79 j ⊆ insert (0, 0) required_79 := by decide
theorem child_envelope_sub_79 : ∀ j, childrenD_79 j ⊆ envelope_79 := by decide
theorem pivot_mem_79 : (0, 0) ∈ envelope_79 := by decide
theorem children_work_79 : ∀ j, Template HasSnaky 3 (childrenC_79 j) (childrenD_79 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 1 (1, 1)).mono (by decide)
· exact (placed_template_map row_works_48 0 (-1, 0)).mono (by decide)
theorem row_works_79 : Template HasSnaky 4 required_79 envelope_79 := by
refine compose HasSnaky 3 childrenC_79 childrenD_79 children_work_79 (0, 0)
required_79 envelope_79 pivot_mem_79 child_required_sub_79 child_envelope_sub_79 ?_
intro b hb; exact common_sub_79 (mem_commonEnvelope childrenD_79 b hb)
def required_80 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_80 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_80 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) required_0), (placedSet 4 (-2, 0) required_13)]
def childrenD_80 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) envelope_0), (placedSet 4 (-2, 0) envelope_13)]
theorem common_sub_80 : commonEnvelope childrenD_80 ⊆ insert (0, 0) required_80 := by decide
theorem child_required_sub_80 : ∀ j, childrenC_80 j ⊆ insert (0, 0) required_80 := by decide
theorem child_envelope_sub_80 : ∀ j, childrenD_80 j ⊆ envelope_80 := by decide
theorem pivot_mem_80 : (0, 0) ∈ envelope_80 := by decide
theorem children_work_80 : ∀ j, Template HasSnaky 3 (childrenC_80 j) (childrenD_80 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 6 (2, 0)).mono (by decide)
· exact (placed_template_map row_works_13 4 (-2, 0)).mono (by decide)
theorem row_works_80 : Template HasSnaky 4 required_80 envelope_80 := by
refine compose HasSnaky 3 childrenC_80 childrenD_80 children_work_80 (0, 0)
required_80 envelope_80 pivot_mem_80 child_required_sub_80 child_envelope_sub_80 ?_
intro b hb; exact common_sub_80 (mem_commonEnvelope childrenD_80 b hb)
end SnakyConditional
end OAI
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