| import OAI.GameTheory.SnakyConditional.Templates.Level08Part01 |
| import OAI.GameTheory.SnakyConditional.Templates.Level08Part02 |
|
|
| namespace OAI |
|
|
| namespace SnakyConditional |
| def required_143 : Finset Cell := ⟨(([(0, 1), (1, 1), (2, 1), (3, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_143 : Finset Cell := ⟨(([(-1, 0), (0, 0), (0, 1), (1, 0), (1, 1), (2, 1), (3, 1), (4, 0), (4, 1), (4, 2), (5, 0), (5, 1), (5, 2), (6, 0), (6, 2)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_143 : Fin 2 → Finset Cell := ![(placedSet 6 (-1, 0) required_6), (placedSet 0 (4, 1) required_108)] |
| def childrenD_143 : Fin 2 → Finset Cell := ![(placedSet 6 (-1, 0) envelope_6), (placedSet 0 (4, 1) envelope_108)] |
| theorem common_sub_143 : commonEnvelope childrenD_143 ⊆ insert (0, 0) required_143 := by decide |
| theorem child_required_sub_143 : ∀ j, childrenC_143 j ⊆ insert (0, 0) required_143 := by decide |
| theorem child_envelope_sub_143 : ∀ j, childrenD_143 j ⊆ envelope_143 := by decide |
| theorem pivot_mem_143 : (0, 0) ∈ envelope_143 := by decide |
| theorem children_work_143 : ∀ j, Template HasSnaky 6 (childrenC_143 j) (childrenD_143 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_6 6 (-1, 0)).mono (by decide) |
| · exact (placed_template_map row_works_108 0 (4, 1)).mono (by decide) |
| theorem row_works_143 : Template HasSnaky 7 required_143 envelope_143 := by |
| refine compose HasSnaky 6 childrenC_143 childrenD_143 children_work_143 (0, 0) |
| required_143 envelope_143 pivot_mem_143 child_required_sub_143 child_envelope_sub_143 ?_ |
| intro b hb |
| def required_164 : Finset Cell := ⟨(([(-1, -3), (-1, -2), (-1, -1), (-1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_164 : Finset Cell := ⟨(([(-2, -1), (-1, -3), (-1, -2), (-1, -1), (-1, 0), (0, 0), (0, 1), (1, 0), (2, -1), (2, 0), (2, 1), (3, -1), (3, 0), (3, 1), (4, -1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_164 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) required_6), (placedSet 0 (1, 0) required_110)] |
| def childrenD_164 : Fin 2 → Finset Cell := ![(placedSet 1 (0, 1) envelope_6), (placedSet 0 (1, 0) envelope_110)] |
| theorem common_sub_164 : commonEnvelope childrenD_164 ⊆ insert (0, 0) required_164 := by decide |
| theorem child_required_sub_164 : ∀ j, childrenC_164 j ⊆ insert (0, 0) required_164 := by decide |
| theorem child_envelope_sub_164 : ∀ j, childrenD_164 j ⊆ envelope_164 := by decide |
| theorem pivot_mem_164 : (0, 0) ∈ envelope_164 := by decide |
| theorem children_work_164 : ∀ j, Template HasSnaky 6 (childrenC_164 j) (childrenD_164 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_110 0 (1, 0)).mono (by decide) |
| theorem row_works_164 : Template HasSnaky 7 required_164 envelope_164 := by |
| refine compose HasSnaky 6 childrenC_164 childrenD_164 children_work_164 (0, 0) |
| required_164 envelope_164 pivot_mem_164 child_required_sub_164 child_envelope_sub_164 ?_ |
| intro b hb |
| def required_165 : Finset Cell := ⟨(([(0, 1), (1, 1), (1, 2), (1, 3), (2, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_165 : Finset Cell := ⟨(([(-1, 0), (0, 0), (0, 1), (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (5, 0), (5, 2)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_165 : Fin 2 → Finset Cell := ![(placedSet 7 (1, 4) required_0), (placedSet 0 (3, 1) required_107)] |
| def childrenD_165 : Fin 2 → Finset Cell := ![(placedSet 7 (1, 4) envelope_0), (placedSet 0 (3, 1) envelope_107)] |
| theorem common_sub_165 : commonEnvelope childrenD_165 ⊆ insert (0, 0) required_165 := by decide |
| theorem child_required_sub_165 : ∀ j, childrenC_165 j ⊆ insert (0, 0) required_165 := by decide |
| theorem child_envelope_sub_165 : ∀ j, childrenD_165 j ⊆ envelope_165 := by decide |
| theorem pivot_mem_165 : (0, 0) ∈ envelope_165 := by decide |
| theorem children_work_165 : ∀ j, Template HasSnaky 6 (childrenC_165 j) (childrenD_165 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_0 7 (1, 4)).mono (by decide) |
| · exact (placed_template_map row_works_107 0 (3, 1)).mono (by decide) |
| theorem row_works_165 : Template HasSnaky 7 required_165 envelope_165 := by |
| refine compose HasSnaky 6 childrenC_165 childrenD_165 children_work_165 (0, 0) |
| required_165 envelope_165 pivot_mem_165 child_required_sub_165 child_envelope_sub_165 ?_ |
| intro b hb |
| def required_166 : Finset Cell := ⟨(([(-1, -1), (-1, 0), (0, 2), (0, 3), (1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_166 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, -1), (2, 0), (2, 1), (3, -1), (3, 0), (3, 1), (4, -1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_166 : Fin 2 → Finset Cell := ![(placedSet 7 (0, 1) required_2), (placedSet 0 (2, 0) required_107)] |
| def childrenD_166 : Fin 2 → Finset Cell := ![(placedSet 7 (0, 1) envelope_2), (placedSet 0 (2, 0) envelope_107)] |
| theorem common_sub_166 : commonEnvelope childrenD_166 ⊆ insert (0, 0) required_166 := by decide |
| theorem child_required_sub_166 : ∀ j, childrenC_166 j ⊆ insert (0, 0) required_166 := by decide |
| theorem child_envelope_sub_166 : ∀ j, childrenD_166 j ⊆ envelope_166 := by decide |
| theorem pivot_mem_166 : (0, 0) ∈ envelope_166 := by decide |
| theorem children_work_166 : ∀ j, Template HasSnaky 6 (childrenC_166 j) (childrenD_166 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_107 0 (2, 0)).mono (by decide) |
| theorem row_works_166 : Template HasSnaky 7 required_166 envelope_166 := by |
| refine compose HasSnaky 6 childrenC_166 childrenD_166 children_work_166 (0, 0) |
| required_166 envelope_166 pivot_mem_166 child_required_sub_166 child_envelope_sub_166 ?_ |
| intro b hb |
| def required_168 : Finset Cell := ⟨(([(0, -3), (0, -2), (0, -1), (1, 0), (3, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_168 : Finset Cell := ⟨(([(-1, 0), (-1, 1), (0, -3), (0, -2), (0, -1), (0, 0), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1), (3, -1), (3, 0), (3, 1), (4, -1), (4, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_168 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 1) required_6), (placedSet 0 (-1, 0) required_152)] |
| def childrenD_168 : Fin 2 → Finset Cell := ![(placedSet 1 (1, 1) envelope_6), (placedSet 0 (-1, 0) envelope_152)] |
| theorem common_sub_168 : commonEnvelope childrenD_168 ⊆ insert (0, 0) required_168 := by decide |
| theorem child_required_sub_168 : ∀ j, childrenC_168 j ⊆ insert (0, 0) required_168 := by decide |
| theorem child_envelope_sub_168 : ∀ j, childrenD_168 j ⊆ envelope_168 := by decide |
| theorem pivot_mem_168 : (0, 0) ∈ envelope_168 := by decide |
| theorem children_work_168 : ∀ j, Template HasSnaky 6 (childrenC_168 j) (childrenD_168 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_152 0 (-1, 0)).mono (by decide) |
| theorem row_works_168 : Template HasSnaky 7 required_168 envelope_168 := by |
| refine compose HasSnaky 6 childrenC_168 childrenD_168 children_work_168 (0, 0) |
| required_168 envelope_168 pivot_mem_168 child_required_sub_168 child_envelope_sub_168 ?_ |
| intro b hb |
| def required_179 : Finset Cell := ⟨(([(-3, -1), (-3, 0), (-2, 0), (-1, -1), (-1, 0), (-1, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_179 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-3, 0), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (2, 0), (3, -1), (3, 0), (4, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_179 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) required_6), (placedSet 5 (1, 0) required_148)] |
| def childrenD_179 : Fin 2 → Finset Cell := ![(placedSet 6 (-4, -1) envelope_6), (placedSet 5 (1, 0) envelope_148)] |
| theorem common_sub_179 : commonEnvelope childrenD_179 ⊆ insert (0, 0) required_179 := by decide |
| theorem child_required_sub_179 : ∀ j, childrenC_179 j ⊆ insert (0, 0) required_179 := by decide |
| theorem child_envelope_sub_179 : ∀ j, childrenD_179 j ⊆ envelope_179 := by decide |
| theorem pivot_mem_179 : (0, 0) ∈ envelope_179 := by decide |
| theorem children_work_179 : ∀ j, Template HasSnaky 6 (childrenC_179 j) (childrenD_179 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_148 5 (1, 0)).mono (by decide) |
| theorem row_works_179 : Template HasSnaky 7 required_179 envelope_179 := by |
| refine compose HasSnaky 6 childrenC_179 childrenD_179 children_work_179 (0, 0) |
| required_179 envelope_179 pivot_mem_179 child_required_sub_179 child_envelope_sub_179 ?_ |
| intro b hb |
| end SnakyConditional |
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| end OAI |
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