File size: 11,561 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.Level07Part01
import OAI.GameTheory.SnakyConditional.Templates.Level07Part02
import OAI.GameTheory.SnakyConditional.Templates.Level07Part03
import OAI.GameTheory.SnakyConditional.Templates.Level07Part04
import OAI.GameTheory.SnakyConditional.Templates.Level07Part05
namespace OAI
namespace SnakyConditional
def required_198 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, 0), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_198 : Finset Cell := ⟨(([(-5, 1), (-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_198 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) required_7), (placedSet 1 (1, 0) required_131)]
def childrenD_198 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) envelope_7), (placedSet 1 (1, 0) envelope_131)]
theorem common_sub_198 : commonEnvelope childrenD_198 ⊆ insert (0, 0) required_198 := by decide
theorem child_required_sub_198 : ∀ j, childrenC_198 j ⊆ insert (0, 0) required_198 := by decide
theorem child_envelope_sub_198 : ∀ j, childrenD_198 j ⊆ envelope_198 := by decide
theorem pivot_mem_198 : (0, 0) ∈ envelope_198 := by decide
theorem children_work_198 : ∀ j, Template HasSnaky 5 (childrenC_198 j) (childrenD_198 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_131 1 (1, 0)).mono (by decide)
theorem row_works_198 : Template HasSnaky 6 required_198 envelope_198 := by
refine compose HasSnaky 5 childrenC_198 childrenD_198 children_work_198 (0, 0)
required_198 envelope_198 pivot_mem_198 child_required_sub_198 child_envelope_sub_198 ?_
intro b hb; exact common_sub_198 (mem_commonEnvelope childrenD_198 b hb)
def required_199 : Finset Cell := ⟨(([(-1, -1), (0, -3), (0, -2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_199 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -4), (1, -3), (1, -2), (1, 0), (1, 1), (1, 2), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_199 : Fin 3 → Finset Cell := ![(placedSet 1 (0, 1) required_55), (placedSet 3 (1, -3) required_64), (placedSet 0 (-1, 0) required_84)]
def childrenD_199 : Fin 3 → Finset Cell := ![(placedSet 1 (0, 1) envelope_55), (placedSet 3 (1, -3) envelope_64), (placedSet 0 (-1, 0) envelope_84)]
theorem common_sub_199 : commonEnvelope childrenD_199 ⊆ insert (0, 0) required_199 := by decide
theorem child_required_sub_199 : ∀ j, childrenC_199 j ⊆ insert (0, 0) required_199 := by decide
theorem child_envelope_sub_199 : ∀ j, childrenD_199 j ⊆ envelope_199 := by decide
theorem pivot_mem_199 : (0, 0) ∈ envelope_199 := by decide
theorem children_work_199 : ∀ j, Template HasSnaky 5 (childrenC_199 j) (childrenD_199 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_55 1 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_64 3 (1, -3)).mono (by decide)
· exact (placed_template_map row_works_84 0 (-1, 0)).mono (by decide)
theorem row_works_199 : Template HasSnaky 6 required_199 envelope_199 := by
refine compose HasSnaky 5 childrenC_199 childrenD_199 children_work_199 (0, 0)
required_199 envelope_199 pivot_mem_199 child_required_sub_199 child_envelope_sub_199 ?_
intro b hb; exact common_sub_199 (mem_commonEnvelope childrenD_199 b hb)
def required_200 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (2, -1)] : List Cell) : Multiset Cell), by decide⟩
def envelope_200 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (-1, 1), (-1, 2), (0, -3), (0, -2), (0, -1), (0, 0), (0, 1), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0), (1, 1), (1, 2), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_200 : Fin 3 → Finset Cell := ![(placedSet 0 (-1, 0) required_103), (placedSet 3 (1, -3) required_64), (placedSet 1 (0, 1) required_55)]
def childrenD_200 : Fin 3 → Finset Cell := ![(placedSet 0 (-1, 0) envelope_103), (placedSet 3 (1, -3) envelope_64), (placedSet 1 (0, 1) envelope_55)]
theorem common_sub_200 : commonEnvelope childrenD_200 ⊆ insert (0, 0) required_200 := by decide
theorem child_required_sub_200 : ∀ j, childrenC_200 j ⊆ insert (0, 0) required_200 := by decide
theorem child_envelope_sub_200 : ∀ j, childrenD_200 j ⊆ envelope_200 := by decide
theorem pivot_mem_200 : (0, 0) ∈ envelope_200 := by decide
theorem children_work_200 : ∀ j, Template HasSnaky 5 (childrenC_200 j) (childrenD_200 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_103 0 (-1, 0)).mono (by decide)
· exact (placed_template_map row_works_64 3 (1, -3)).mono (by decide)
· exact (placed_template_map row_works_55 1 (0, 1)).mono (by decide)
theorem row_works_200 : Template HasSnaky 6 required_200 envelope_200 := by
refine compose HasSnaky 5 childrenC_200 childrenD_200 children_work_200 (0, 0)
required_200 envelope_200 pivot_mem_200 child_required_sub_200 child_envelope_sub_200 ?_
intro b hb; exact common_sub_200 (mem_commonEnvelope childrenD_200 b hb)
def required_206 : Finset Cell := ⟨(([(0, 2), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_206 : Finset Cell := ⟨(([(-2, 0), (-1, 0), (-1, 1), (0, 0), (0, 1), (0, 2), (0, 3), (1, -1), (1, 0), (2, -1), (2, 0), (3, -1), (3, 0), (4, -1), (4, 0), (5, -1), (5, 0), (6, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_206 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_28), (placedSet 2 (4, 0) required_135)]
def childrenD_206 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_28), (placedSet 2 (4, 0) envelope_135)]
theorem common_sub_206 : commonEnvelope childrenD_206 ⊆ insert (0, 0) required_206 := by decide
theorem child_required_sub_206 : ∀ j, childrenC_206 j ⊆ insert (0, 0) required_206 := by decide
theorem child_envelope_sub_206 : ∀ j, childrenD_206 j ⊆ envelope_206 := by decide
theorem pivot_mem_206 : (0, 0) ∈ envelope_206 := by decide
theorem children_work_206 : ∀ j, Template HasSnaky 5 (childrenC_206 j) (childrenD_206 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_28 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_135 2 (4, 0)).mono (by decide)
theorem row_works_206 : Template HasSnaky 6 required_206 envelope_206 := by
refine compose HasSnaky 5 childrenC_206 childrenD_206 children_work_206 (0, 0)
required_206 envelope_206 pivot_mem_206 child_required_sub_206 child_envelope_sub_206 ?_
intro b hb; exact common_sub_206 (mem_commonEnvelope childrenD_206 b hb)
def required_207 : Finset Cell := ⟨(([(0, 2), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_207 : Finset Cell := ⟨(([(-1, 1), (0, 0), (0, 1), (0, 2), (0, 3), (1, -1), (1, 0), (2, -1), (2, 0), (3, 0), (3, 1), (4, -1), (4, 0), (4, 1), (5, -1), (5, 0), (5, 1), (6, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_207 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) required_28), (placedSet 0 (4, 0) required_127)]
def childrenD_207 : Fin 2 → Finset Cell := ![(placedSet 3 (0, 1) envelope_28), (placedSet 0 (4, 0) envelope_127)]
theorem common_sub_207 : commonEnvelope childrenD_207 ⊆ insert (0, 0) required_207 := by decide
theorem child_required_sub_207 : ∀ j, childrenC_207 j ⊆ insert (0, 0) required_207 := by decide
theorem child_envelope_sub_207 : ∀ j, childrenD_207 j ⊆ envelope_207 := by decide
theorem pivot_mem_207 : (0, 0) ∈ envelope_207 := by decide
theorem children_work_207 : ∀ j, Template HasSnaky 5 (childrenC_207 j) (childrenD_207 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_28 3 (0, 1)).mono (by decide)
· exact (placed_template_map row_works_127 0 (4, 0)).mono (by decide)
theorem row_works_207 : Template HasSnaky 6 required_207 envelope_207 := by
refine compose HasSnaky 5 childrenC_207 childrenD_207 children_work_207 (0, 0)
required_207 envelope_207 pivot_mem_207 child_required_sub_207 child_envelope_sub_207 ?_
intro b hb; exact common_sub_207 (mem_commonEnvelope childrenD_207 b hb)
def required_208 : Finset Cell := ⟨(([(-4, 0), (-3, 0), (-2, -1), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩
def envelope_208 : Finset Cell := ⟨(([(-5, 1), (-4, 0), (-4, 1), (-3, 0), (-3, 1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_208 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) required_7), (placedSet 0 (1, 0) required_127)]
def childrenD_208 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) envelope_7), (placedSet 0 (1, 0) envelope_127)]
theorem common_sub_208 : commonEnvelope childrenD_208 ⊆ insert (0, 0) required_208 := by decide
theorem child_required_sub_208 : ∀ j, childrenC_208 j ⊆ insert (0, 0) required_208 := by decide
theorem child_envelope_sub_208 : ∀ j, childrenD_208 j ⊆ envelope_208 := by decide
theorem pivot_mem_208 : (0, 0) ∈ envelope_208 := by decide
theorem children_work_208 : ∀ j, Template HasSnaky 5 (childrenC_208 j) (childrenD_208 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_127 0 (1, 0)).mono (by decide)
theorem row_works_208 : Template HasSnaky 6 required_208 envelope_208 := by
refine compose HasSnaky 5 childrenC_208 childrenD_208 children_work_208 (0, 0)
required_208 envelope_208 pivot_mem_208 child_required_sub_208 child_envelope_sub_208 ?_
intro b hb; exact common_sub_208 (mem_commonEnvelope childrenD_208 b hb)
def required_210 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (-1, 2)] : List Cell) : Multiset Cell), by decide⟩
def envelope_210 : Finset Cell := ⟨(([(-3, 0), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (-1, 2), (-1, 3), (0, -1), (0, 0), (0, 1), (0, 2), (0, 3), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1)] : List Cell) : Multiset Cell), by decide⟩
def childrenC_210 : Fin 3 → Finset Cell := ![(placedSet 2 (1, 0) required_58), (placedSet 0 (1, 0) required_57), (placedSet 1 (0, 1) required_117)]
def childrenD_210 : Fin 3 → Finset Cell := ![(placedSet 2 (1, 0) envelope_58), (placedSet 0 (1, 0) envelope_57), (placedSet 1 (0, 1) envelope_117)]
theorem common_sub_210 : commonEnvelope childrenD_210 ⊆ insert (0, 0) required_210 := by decide
theorem child_required_sub_210 : ∀ j, childrenC_210 j ⊆ insert (0, 0) required_210 := by decide
theorem child_envelope_sub_210 : ∀ j, childrenD_210 j ⊆ envelope_210 := by decide
theorem pivot_mem_210 : (0, 0) ∈ envelope_210 := by decide
theorem children_work_210 : ∀ j, Template HasSnaky 5 (childrenC_210 j) (childrenD_210 j) := by
intro j
fin_cases j
· exact (placed_template_map row_works_58 2 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_57 0 (1, 0)).mono (by decide)
· exact (placed_template_map row_works_117 1 (0, 1)).mono (by decide)
theorem row_works_210 : Template HasSnaky 6 required_210 envelope_210 := by
refine compose HasSnaky 5 childrenC_210 childrenD_210 children_work_210 (0, 0)
required_210 envelope_210 pivot_mem_210 child_required_sub_210 child_envelope_sub_210 ?_
intro b hb; exact common_sub_210 (mem_commonEnvelope childrenD_210 b hb)
end SnakyConditional
end OAI
|