| import OAI.GameTheory.SnakyConditional.Templates.Level07Part04 |
| import OAI.GameTheory.SnakyConditional.Templates.Level07Part08 |
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|
| namespace OAI |
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| namespace SnakyConditional |
| def required_293 : Finset Cell := ⟨(([(-2, -2), (-1, -3), (-1, -2), (0, -2), (0, 1), (1, -2)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_293 : Finset Cell := ⟨(([(-3, -1), (-3, 1), (-2, -2), (-2, -1), (-2, 0), (-2, 1), (-1, -3), (-1, -2), (-1, 0), (-1, 1), (0, -2), (0, -1), (0, 0), (0, 1), (1, -3), (1, -2), (1, -1), (1, 0), (2, -2), (2, -1), (2, 0), (3, -1), (3, 0), (4, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_293 : Fin 2 → Finset Cell := ![(placedSet 7 (0, -1) required_2), (placedSet 0 (1, 0) required_280)] |
| def childrenD_293 : Fin 2 → Finset Cell := ![(placedSet 7 (0, -1) envelope_2), (placedSet 0 (1, 0) envelope_280)] |
| theorem common_sub_293 : commonEnvelope childrenD_293 ⊆ insert (0, 0) required_293 := by decide |
| theorem child_required_sub_293 : ∀ j, childrenC_293 j ⊆ insert (0, 0) required_293 := by decide |
| theorem child_envelope_sub_293 : ∀ j, childrenD_293 j ⊆ envelope_293 := by decide |
| theorem pivot_mem_293 : (0, 0) ∈ envelope_293 := by decide |
| theorem children_work_293 : ∀ j, Template HasSnaky 5 (childrenC_293 j) (childrenD_293 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_280 0 (1, 0)).mono (by decide) |
| theorem row_works_293 : Template HasSnaky 6 required_293 envelope_293 := by |
| refine compose HasSnaky 5 childrenC_293 childrenD_293 children_work_293 (0, 0) |
| required_293 envelope_293 pivot_mem_293 child_required_sub_293 child_envelope_sub_293 ?_ |
| intro b hb; exact common_sub_293 (mem_commonEnvelope childrenD_293 b hb) |
| def required_429 : Finset Cell := ⟨(([(0, 2), (1, -1), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_429 : 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), (3, 1), (4, 0), (4, 1), (5, 0), (5, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_429 : Fin 2 → Finset Cell := ![(placedSet 0 (2, -1) required_128), (placedSet 3 (0, 1) required_28)] |
| def childrenD_429 : Fin 2 → Finset Cell := ![(placedSet 0 (2, -1) envelope_128), (placedSet 3 (0, 1) envelope_28)] |
| theorem common_sub_429 : commonEnvelope childrenD_429 ⊆ insert (0, 0) required_429 := by decide |
| theorem child_required_sub_429 : ∀ j, childrenC_429 j ⊆ insert (0, 0) required_429 := by decide |
| theorem child_envelope_sub_429 : ∀ j, childrenD_429 j ⊆ envelope_429 := by decide |
| theorem pivot_mem_429 : (0, 0) ∈ envelope_429 := by decide |
| theorem children_work_429 : ∀ j, Template HasSnaky 5 (childrenC_429 j) (childrenD_429 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_128 0 (2, -1)).mono (by decide) |
| · exact (placed_template_map row_works_28 3 (0, 1)).mono (by decide) |
| theorem row_works_429 : Template HasSnaky 6 required_429 envelope_429 := by |
| refine compose HasSnaky 5 childrenC_429 childrenD_429 children_work_429 (0, 0) |
| required_429 envelope_429 pivot_mem_429 child_required_sub_429 child_envelope_sub_429 ?_ |
| intro b hb; exact common_sub_429 (mem_commonEnvelope childrenD_429 b hb) |
| end SnakyConditional |
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| end OAI |
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