| import OAI.GameTheory.SnakyConditional.Templates.Level03Part01 |
|
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| namespace OAI |
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| namespace SnakyConditional |
| def required_52 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (0, -1), (1, -1), (2, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_52 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_52 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) required_0), (placedSet 4 (3, -1) required_0)] |
| def childrenD_52 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) envelope_0), (placedSet 4 (3, -1) envelope_0)] |
| theorem common_sub_52 : commonEnvelope childrenD_52 ⊆ insert (0, 0) required_52 := by decide |
| theorem child_required_sub_52 : ∀ j, childrenC_52 j ⊆ insert (0, 0) required_52 := by decide |
| theorem child_envelope_sub_52 : ∀ j, childrenD_52 j ⊆ envelope_52 := by decide |
| theorem pivot_mem_52 : (0, 0) ∈ envelope_52 := by decide |
| theorem children_work_52 : ∀ j, Template HasSnaky 1 (childrenC_52 j) (childrenD_52 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_0 0 (-4, -1)).mono (by decide) |
| · exact (placed_template_map row_works_0 4 (3, -1)).mono (by decide) |
| theorem row_works_52 : Template HasSnaky 2 required_52 envelope_52 := by |
| refine compose HasSnaky 1 childrenC_52 childrenD_52 children_work_52 (0, 0) |
| required_52 envelope_52 pivot_mem_52 child_required_sub_52 child_envelope_sub_52 ?_ |
| intro b hb; exact common_sub_52 (mem_commonEnvelope childrenD_52 b hb) |
| end SnakyConditional |
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| end OAI |
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