| import OAI.GameTheory.SnakyConditional.Templates.Level03Part01 |
| import OAI.GameTheory.SnakyConditional.Templates.Level03Part04 |
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|
| namespace OAI |
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|
| namespace SnakyConditional |
| def required_15 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_15 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_15 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) required_0), (placedSet 6 (-2, 0) required_3)] |
| def childrenD_15 : Fin 2 → Finset Cell := ![(placedSet 6 (2, 0) envelope_0), (placedSet 6 (-2, 0) envelope_3)] |
| theorem common_sub_15 : commonEnvelope childrenD_15 ⊆ insert (0, 0) required_15 := by decide |
| theorem child_required_sub_15 : ∀ j, childrenC_15 j ⊆ insert (0, 0) required_15 := by decide |
| theorem child_envelope_sub_15 : ∀ j, childrenD_15 j ⊆ envelope_15 := by decide |
| theorem pivot_mem_15 : (0, 0) ∈ envelope_15 := by decide |
| theorem children_work_15 : ∀ j, Template HasSnaky 1 (childrenC_15 j) (childrenD_15 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_3 6 (-2, 0)).mono (by decide) |
| theorem row_works_15 : Template HasSnaky 2 required_15 envelope_15 := by |
| refine compose HasSnaky 1 childrenC_15 childrenD_15 children_work_15 (0, 0) |
| required_15 envelope_15 pivot_mem_15 child_required_sub_15 child_envelope_sub_15 ?_ |
| intro b hb; exact common_sub_15 (mem_commonEnvelope childrenD_15 b hb) |
| def required_16 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (0, -1), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_16 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, 0), (2, 0), (3, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_16 : Fin 2 → Finset Cell := ![(placedSet 6 (-1, 0) required_3), (placedSet 6 (3, 0) required_0)] |
| def childrenD_16 : Fin 2 → Finset Cell := ![(placedSet 6 (-1, 0) envelope_3), (placedSet 6 (3, 0) envelope_0)] |
| theorem common_sub_16 : commonEnvelope childrenD_16 ⊆ insert (0, 0) required_16 := by decide |
| theorem child_required_sub_16 : ∀ j, childrenC_16 j ⊆ insert (0, 0) required_16 := by decide |
| theorem child_envelope_sub_16 : ∀ j, childrenD_16 j ⊆ envelope_16 := by decide |
| theorem pivot_mem_16 : (0, 0) ∈ envelope_16 := by decide |
| theorem children_work_16 : ∀ j, Template HasSnaky 1 (childrenC_16 j) (childrenD_16 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_3 6 (-1, 0)).mono (by decide) |
| · exact (placed_template_map row_works_0 6 (3, 0)).mono (by decide) |
| theorem row_works_16 : Template HasSnaky 2 required_16 envelope_16 := by |
| refine compose HasSnaky 1 childrenC_16 childrenD_16 children_work_16 (0, 0) |
| required_16 envelope_16 pivot_mem_16 child_required_sub_16 child_envelope_sub_16 ?_ |
| intro b hb; exact common_sub_16 (mem_commonEnvelope childrenD_16 b hb) |
| end SnakyConditional |
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| end OAI |
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