File size: 10,423 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 | import OAI.GameTheory.SnakyConditional.Templates.Level06Part01
import OAI.GameTheory.SnakyConditional.Templates.Level06Part02
import OAI.GameTheory.SnakyConditional.Templates.Level06Part03
namespace OAI
namespace SnakyConditional
def required_84 : Finset Cell := ⟨(([(0, -1), (1, -3), (1, -2), (1, -1), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_84 : Finset Cell := ⟨(([(-1, -1), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, 0), (2, 1), (3, 0), (4, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_84 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 0 (2, 0) required_67)]
def childrenD_84 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 0 (2, 0) envelope_67)]
theorem common_sub_84 : commonEnvelope childrenD_84 ⊆ insert (0, 0) required_84 := by decide
theorem child_required_sub_84 : ∀ j, childrenC_84 j ⊆ insert (0, 0) required_84 := by decide
theorem child_envelope_sub_84 : ∀ j, childrenD_84 j ⊆ envelope_84 := by decide
theorem pivot_mem_84 : (0, 0) ∈ envelope_84 := by decide
theorem children_work_84 : ∀ j, Template HasSnaky 4 (childrenC_84 j) (childrenD_84 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_67 0 (2, 0)).mono (by decide)
theorem row_works_84 : Template HasSnaky 5 required_84 envelope_84 := by
refine compose HasSnaky 4 childrenC_84 childrenD_84 children_work_84 (0, 0)
required_84 envelope_84 pivot_mem_84 child_required_sub_84 child_envelope_sub_84 ?_
intro b hb; exact common_sub_84 (mem_commonEnvelope childrenD_84 b hb)
def required_86 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-2, -1), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_86 : Finset Cell := ⟨(([(-4, 1), (-3, -1), (-3, 0), (-3, 1), (-3, 2), (-3, 3), (-2, -2), (-2, -1), (-2, 0), (-1, 0), (0, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_86 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) required_0), (placedSet 3 (-3, 1) required_67)]
def childrenD_86 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) envelope_0), (placedSet 3 (-3, 1) envelope_67)]
theorem common_sub_86 : commonEnvelope childrenD_86 ⊆ insert (0, 0) required_86 := by decide
theorem child_required_sub_86 : ∀ j, childrenC_86 j ⊆ insert (0, 0) required_86 := by decide
theorem child_envelope_sub_86 : ∀ j, childrenD_86 j ⊆ envelope_86 := by decide
theorem pivot_mem_86 : (0, 0) ∈ envelope_86 := by decide
theorem children_work_86 : ∀ j, Template HasSnaky 4 (childrenC_86 j) (childrenD_86 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_0 6 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_67 3 (-3, 1)).mono (by decide)
theorem row_works_86 : Template HasSnaky 5 required_86 envelope_86 := by
refine compose HasSnaky 4 childrenC_86 childrenD_86 children_work_86 (0, 0)
required_86 envelope_86 pivot_mem_86 child_required_sub_86 child_envelope_sub_86 ?_
intro b hb; exact common_sub_86 (mem_commonEnvelope childrenD_86 b hb)
def required_88 : Finset Cell := ⟨(([(-2, -1), (-2, 0), (-1, -1), (-1, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_88 : Finset Cell := ⟨(([(-3, 1), (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-2, 3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_88 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) required_0), (placedSet 3 (-2, 1) required_67)]
def childrenD_88 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) envelope_0), (placedSet 3 (-2, 1) envelope_67)]
theorem common_sub_88 : commonEnvelope childrenD_88 ⊆ insert (0, 0) required_88 := by decide
theorem child_required_sub_88 : ∀ j, childrenC_88 j ⊆ insert (0, 0) required_88 := by decide
theorem child_envelope_sub_88 : ∀ j, childrenD_88 j ⊆ envelope_88 := by decide
theorem pivot_mem_88 : (0, 0) ∈ envelope_88 := by decide
theorem children_work_88 : ∀ j, Template HasSnaky 4 (childrenC_88 j) (childrenD_88 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_67 3 (-2, 1)).mono (by decide)
theorem row_works_88 : Template HasSnaky 5 required_88 envelope_88 := by
refine compose HasSnaky 4 childrenC_88 childrenD_88 children_work_88 (0, 0)
required_88 envelope_88 pivot_mem_88 child_required_sub_88 child_envelope_sub_88 ?_
intro b hb; exact common_sub_88 (mem_commonEnvelope childrenD_88 b hb)
def required_91 : Finset Cell := ⟨(([(1, -3), (1, -2), (1, -1), (1, 0), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_91 : Finset Cell := ⟨(([(0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, -1), (2, 0), (2, 1), (3, -1), (3, 0), (4, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_91 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_6), (placedSet 5 (3, -1) required_74)]
def childrenD_91 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_6), (placedSet 5 (3, -1) envelope_74)]
theorem common_sub_91 : commonEnvelope childrenD_91 ⊆ insert (0, 0) required_91 := by decide
theorem child_required_sub_91 : ∀ j, childrenC_91 j ⊆ insert (0, 0) required_91 := by decide
theorem child_envelope_sub_91 : ∀ j, childrenD_91 j ⊆ envelope_91 := by decide
theorem pivot_mem_91 : (0, 0) ∈ envelope_91 := by decide
theorem children_work_91 : ∀ j, Template HasSnaky 4 (childrenC_91 j) (childrenD_91 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_74 5 (3, -1)).mono (by decide)
theorem row_works_91 : Template HasSnaky 5 required_91 envelope_91 := by
refine compose HasSnaky 4 childrenC_91 childrenD_91 children_work_91 (0, 0)
required_91 envelope_91 pivot_mem_91 child_required_sub_91 child_envelope_sub_91 ?_
intro b hb; exact common_sub_91 (mem_commonEnvelope childrenD_91 b hb)
def required_96 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_96 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_96 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 1) required_6), (placedSet 0 (-1, 1) required_70)]
def childrenD_96 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 1) envelope_6), (placedSet 0 (-1, 1) envelope_70)]
theorem common_sub_96 : commonEnvelope childrenD_96 ⊆ insert (0, 0) required_96 := by decide
theorem child_required_sub_96 : ∀ j, childrenC_96 j ⊆ insert (0, 0) required_96 := by decide
theorem child_envelope_sub_96 : ∀ j, childrenD_96 j ⊆ envelope_96 := by decide
theorem pivot_mem_96 : (0, 0) ∈ envelope_96 := by decide
theorem children_work_96 : ∀ j, Template HasSnaky 4 (childrenC_96 j) (childrenD_96 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_70 0 (-1, 1)).mono (by decide)
theorem row_works_96 : Template HasSnaky 5 required_96 envelope_96 := by
refine compose HasSnaky 4 childrenC_96 childrenD_96 children_work_96 (0, 0)
required_96 envelope_96 pivot_mem_96 child_required_sub_96 child_envelope_sub_96 ?_
intro b hb; exact common_sub_96 (mem_commonEnvelope childrenD_96 b hb)
def required_97 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-3, 1), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_97 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-3, 0), (-3, 1), (-2, 0), (-2, 1), (-1, 0), (0, 0), (0, 1), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_97 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) required_6), (placedSet 0 (1, 0) required_44)]
def childrenD_97 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) envelope_6), (placedSet 0 (1, 0) envelope_44)]
theorem common_sub_97 : commonEnvelope childrenD_97 ⊆ insert (0, 0) required_97 := by decide
theorem child_required_sub_97 : ∀ j, childrenC_97 j ⊆ insert (0, 0) required_97 := by decide
theorem child_envelope_sub_97 : ∀ j, childrenD_97 j ⊆ envelope_97 := by decide
theorem pivot_mem_97 : (0, 0) ∈ envelope_97 := by decide
theorem children_work_97 : ∀ j, Template HasSnaky 4 (childrenC_97 j) (childrenD_97 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_44 0 (1, 0)).mono (by decide)
theorem row_works_97 : Template HasSnaky 5 required_97 envelope_97 := by
refine compose HasSnaky 4 childrenC_97 childrenD_97 children_work_97 (0, 0)
required_97 envelope_97 pivot_mem_97 child_required_sub_97 child_envelope_sub_97 ?_
intro b hb; exact common_sub_97 (mem_commonEnvelope childrenD_97 b hb)
def required_98 : Finset Cell := ⟨(([(-1, -1), (-1, 0), (-1, 1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_98 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_98 : Fin 2 → Finset Cell := ![(placedSet 6 (-2, -1) required_6), (placedSet 0 (3, 0) required_44)]
def childrenD_98 : Fin 2 → Finset Cell := ![(placedSet 6 (-2, -1) envelope_6), (placedSet 0 (3, 0) envelope_44)]
theorem common_sub_98 : commonEnvelope childrenD_98 ⊆ insert (0, 0) required_98 := by decide
theorem child_required_sub_98 : ∀ j, childrenC_98 j ⊆ insert (0, 0) required_98 := by decide
theorem child_envelope_sub_98 : ∀ j, childrenD_98 j ⊆ envelope_98 := by decide
theorem pivot_mem_98 : (0, 0) ∈ envelope_98 := by decide
theorem children_work_98 : ∀ j, Template HasSnaky 4 (childrenC_98 j) (childrenD_98 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_6 6 (-2, -1)).mono (by decide)
· exact (placed_template_map row_works_44 0 (3, 0)).mono (by decide)
theorem row_works_98 : Template HasSnaky 5 required_98 envelope_98 := by
refine compose HasSnaky 4 childrenC_98 childrenD_98 children_work_98 (0, 0)
required_98 envelope_98 pivot_mem_98 child_required_sub_98 child_envelope_sub_98 ?_
intro b hb; exact common_sub_98 (mem_commonEnvelope childrenD_98 b hb)
end SnakyConditional
end OAI
|