File size: 10,932 Bytes
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 | import OAI.GameTheory.SnakyConditional.Templates.Level05Part01
import OAI.GameTheory.SnakyConditional.Templates.Level05Part02
import OAI.GameTheory.SnakyConditional.Templates.Level05Part04
import OAI.GameTheory.SnakyConditional.Templates.Level05Part05
import OAI.GameTheory.SnakyConditional.Templates.Level05Part06
import OAI.GameTheory.SnakyConditional.Templates.Level05Part07
namespace OAI
namespace SnakyConditional
def required_81 : Finset Cell := ⟨(([(1, -4), (1, -3), (1, -2), (1, -1), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_81 : 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_81 : Fin 2 → Finset Cell := ![(placedSet 3 (0, -1) required_4), (placedSet 0 (1, 0) required_43)]
def childrenD_81 : Fin 2 → Finset Cell := ![(placedSet 3 (0, -1) envelope_4), (placedSet 0 (1, 0) envelope_43)]
theorem common_sub_81 : commonEnvelope childrenD_81 ⊆ insert (0, 0) required_81 := by decide
theorem child_required_sub_81 : ∀ j, childrenC_81 j ⊆ insert (0, 0) required_81 := by decide
theorem child_envelope_sub_81 : ∀ j, childrenD_81 j ⊆ envelope_81 := by decide
theorem pivot_mem_81 : (0, 0) ∈ envelope_81 := by decide
theorem children_work_81 : ∀ j, Template HasSnaky 3 (childrenC_81 j) (childrenD_81 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_43 0 (1, 0)).mono (by decide)
theorem row_works_81 : Template HasSnaky 4 required_81 envelope_81 := by
refine compose HasSnaky 3 childrenC_81 childrenD_81 children_work_81 (0, 0)
required_81 envelope_81 pivot_mem_81 child_required_sub_81 child_envelope_sub_81 ?_
intro b hb; exact common_sub_81 (mem_commonEnvelope childrenD_81 b hb)
def required_82 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_82 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_82 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 0 (-3, -1) required_36)]
def childrenD_82 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 0 (-3, -1) envelope_36)]
theorem common_sub_82 : commonEnvelope childrenD_82 ⊆ insert (0, 0) required_82 := by decide
theorem child_required_sub_82 : ∀ j, childrenC_82 j ⊆ insert (0, 0) required_82 := by decide
theorem child_envelope_sub_82 : ∀ j, childrenD_82 j ⊆ envelope_82 := by decide
theorem pivot_mem_82 : (0, 0) ∈ envelope_82 := by decide
theorem children_work_82 : ∀ j, Template HasSnaky 3 (childrenC_82 j) (childrenD_82 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_36 0 (-3, -1)).mono (by decide)
theorem row_works_82 : Template HasSnaky 4 required_82 envelope_82 := by
refine compose HasSnaky 3 childrenC_82 childrenD_82 children_work_82 (0, 0)
required_82 envelope_82 pivot_mem_82 child_required_sub_82 child_envelope_sub_82 ?_
intro b hb; exact common_sub_82 (mem_commonEnvelope childrenD_82 b hb)
def required_85 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (0, -1), (1, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_85 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (2, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_85 : Fin 2 → Finset Cell := ![(placedSet 0 (2, -1) required_9), (placedSet 4 (1, 0) required_8)]
def childrenD_85 : Fin 2 → Finset Cell := ![(placedSet 0 (2, -1) envelope_9), (placedSet 4 (1, 0) envelope_8)]
theorem common_sub_85 : commonEnvelope childrenD_85 ⊆ insert (0, 0) required_85 := by decide
theorem child_required_sub_85 : ∀ j, childrenC_85 j ⊆ insert (0, 0) required_85 := by decide
theorem child_envelope_sub_85 : ∀ j, childrenD_85 j ⊆ envelope_85 := by decide
theorem pivot_mem_85 : (0, 0) ∈ envelope_85 := by decide
theorem children_work_85 : ∀ j, Template HasSnaky 3 (childrenC_85 j) (childrenD_85 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_9 0 (2, -1)).mono (by decide)
· exact (placed_template_map row_works_8 4 (1, 0)).mono (by decide)
theorem row_works_85 : Template HasSnaky 4 required_85 envelope_85 := by
refine compose HasSnaky 3 childrenC_85 childrenD_85 children_work_85 (0, 0)
required_85 envelope_85 pivot_mem_85 child_required_sub_85 child_envelope_sub_85 ?_
intro b hb; exact common_sub_85 (mem_commonEnvelope childrenD_85 b hb)
def required_87 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (-1, 1), (-1, 2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_87 : Finset Cell := ⟨(([(-3, 0), (-2, 0), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_87 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) required_0), (placedSet 2 (1, -1) required_24)]
def childrenD_87 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) envelope_0), (placedSet 2 (1, -1) envelope_24)]
theorem common_sub_87 : commonEnvelope childrenD_87 ⊆ insert (0, 0) required_87 := by decide
theorem child_required_sub_87 : ∀ j, childrenC_87 j ⊆ insert (0, 0) required_87 := by decide
theorem child_envelope_sub_87 : ∀ j, childrenD_87 j ⊆ envelope_87 := by decide
theorem pivot_mem_87 : (0, 0) ∈ envelope_87 := by decide
theorem children_work_87 : ∀ j, Template HasSnaky 3 (childrenC_87 j) (childrenD_87 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_24 2 (1, -1)).mono (by decide)
theorem row_works_87 : Template HasSnaky 4 required_87 envelope_87 := by
refine compose HasSnaky 3 childrenC_87 childrenD_87 children_work_87 (0, 0)
required_87 envelope_87 pivot_mem_87 child_required_sub_87 child_envelope_sub_87 ?_
intro b hb; exact common_sub_87 (mem_commonEnvelope childrenD_87 b hb)
def required_89 : Finset Cell := ⟨(([(-1, -2), (0, -4), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_89 : Finset Cell := ⟨(([(-1, -4), (-1, -3), (-1, -2), (0, -4), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_89 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, -3) required_8), (placedSet 1 (1, 0) required_7)]
def childrenD_89 : Fin 2 → Finset Cell := ![(placedSet 3 (-1, -3) envelope_8), (placedSet 1 (1, 0) envelope_7)]
theorem common_sub_89 : commonEnvelope childrenD_89 ⊆ insert (0, 0) required_89 := by decide
theorem child_required_sub_89 : ∀ j, childrenC_89 j ⊆ insert (0, 0) required_89 := by decide
theorem child_envelope_sub_89 : ∀ j, childrenD_89 j ⊆ envelope_89 := by decide
theorem pivot_mem_89 : (0, 0) ∈ envelope_89 := by decide
theorem children_work_89 : ∀ j, Template HasSnaky 3 (childrenC_89 j) (childrenD_89 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_8 3 (-1, -3)).mono (by decide)
· exact (placed_template_map row_works_7 1 (1, 0)).mono (by decide)
theorem row_works_89 : Template HasSnaky 4 required_89 envelope_89 := by
refine compose HasSnaky 3 childrenC_89 childrenD_89 children_work_89 (0, 0)
required_89 envelope_89 pivot_mem_89 child_required_sub_89 child_envelope_sub_89 ?_
intro b hb; exact common_sub_89 (mem_commonEnvelope childrenD_89 b hb)
def required_90 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_90 : Finset Cell := ⟨(([(-5, -1), (-4, -1), (-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_90 : Fin 4 → Finset Cell := ![(placedSet 0 (-1, -1) required_31), (placedSet 6 (-4, -1) required_54), (placedSet 0 (1, 0) required_54), (placedSet 6 (-2, 0) required_31)]
def childrenD_90 : Fin 4 → Finset Cell := ![(placedSet 0 (-1, -1) envelope_31), (placedSet 6 (-4, -1) envelope_54), (placedSet 0 (1, 0) envelope_54), (placedSet 6 (-2, 0) envelope_31)]
theorem common_sub_90 : commonEnvelope childrenD_90 ⊆ insert (0, 0) required_90 := by decide
theorem child_required_sub_90 : ∀ j, childrenC_90 j ⊆ insert (0, 0) required_90 := by decide
theorem child_envelope_sub_90 : ∀ j, childrenD_90 j ⊆ envelope_90 := by decide
theorem pivot_mem_90 : (0, 0) ∈ envelope_90 := by decide
theorem children_work_90 : ∀ j, Template HasSnaky 3 (childrenC_90 j) (childrenD_90 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_31 0 (-1, -1)).mono (by decide)
· exact (placed_template_map row_works_54 6 (-4, -1)).mono (by decide)
· exact (placed_template_map row_works_54 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_31 6 (-2, 0)).mono (by decide)
theorem row_works_90 : Template HasSnaky 4 required_90 envelope_90 := by
refine compose HasSnaky 3 childrenC_90 childrenD_90 children_work_90 (0, 0)
required_90 envelope_90 pivot_mem_90 child_required_sub_90 child_envelope_sub_90 ?_
intro b hb; exact common_sub_90 (mem_commonEnvelope childrenD_90 b hb)
def required_92 : Finset Cell := ⟨(([(-3, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_92 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, -1), (0, 0), (0, 1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_92 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 0 (-2, -1) required_33)]
def childrenD_92 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 0 (-2, -1) envelope_33)]
theorem common_sub_92 : commonEnvelope childrenD_92 ⊆ insert (0, 0) required_92 := by decide
theorem child_required_sub_92 : ∀ j, childrenC_92 j ⊆ insert (0, 0) required_92 := by decide
theorem child_envelope_sub_92 : ∀ j, childrenD_92 j ⊆ envelope_92 := by decide
theorem pivot_mem_92 : (0, 0) ∈ envelope_92 := by decide
theorem children_work_92 : ∀ j, Template HasSnaky 3 (childrenC_92 j) (childrenD_92 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_33 0 (-2, -1)).mono (by decide)
theorem row_works_92 : Template HasSnaky 4 required_92 envelope_92 := by
refine compose HasSnaky 3 childrenC_92 childrenD_92 children_work_92 (0, 0)
required_92 envelope_92 pivot_mem_92 child_required_sub_92 child_envelope_sub_92 ?_
intro b hb; exact common_sub_92 (mem_commonEnvelope childrenD_92 b hb)
end SnakyConditional
end OAI
|