| import OAI.GameTheory.SnakyConditional.Templates.Level04Part01 |
| import OAI.GameTheory.SnakyConditional.Templates.Level04Part02 |
| import OAI.GameTheory.SnakyConditional.Templates.Level04Part06 |
|
|
| namespace OAI |
|
|
| namespace SnakyConditional |
| def required_77 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (0, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_77 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (0, -1), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_77 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) required_0), (placedSet 0 (1, 0) required_12)] |
| def childrenD_77 : Fin 2 → Finset Cell := ![(placedSet 5 (-1, 3) envelope_0), (placedSet 0 (1, 0) envelope_12)] |
| theorem common_sub_77 : commonEnvelope childrenD_77 ⊆ insert (0, 0) required_77 := by decide |
| theorem child_required_sub_77 : ∀ j, childrenC_77 j ⊆ insert (0, 0) required_77 := by decide |
| theorem child_envelope_sub_77 : ∀ j, childrenD_77 j ⊆ envelope_77 := by decide |
| theorem pivot_mem_77 : (0, 0) ∈ envelope_77 := by decide |
| theorem children_work_77 : ∀ j, Template HasSnaky 2 (childrenC_77 j) (childrenD_77 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_0 5 (-1, 3)).mono (by decide) |
| · exact (placed_template_map row_works_12 0 (1, 0)).mono (by decide) |
| theorem row_works_77 : Template HasSnaky 3 required_77 envelope_77 := by |
| refine compose HasSnaky 2 childrenC_77 childrenD_77 children_work_77 (0, 0) |
| required_77 envelope_77 pivot_mem_77 child_required_sub_77 child_envelope_sub_77 ?_ |
| intro b hb; exact common_sub_77 (mem_commonEnvelope childrenD_77 b hb) |
| def required_78 : Finset Cell := ⟨(([(-2, -1), (-1, -1), (0, -1), (1, -1), (2, -1), (3, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_78 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, -1), (1, 0), (2, -1), (3, -1), (4, -1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_78 : Fin 2 → Finset Cell := ![(placedSet 4 (-1, 0) required_6), (placedSet 0 (1, 0) required_52)] |
| def childrenD_78 : Fin 2 → Finset Cell := ![(placedSet 4 (-1, 0) envelope_6), (placedSet 0 (1, 0) envelope_52)] |
| theorem common_sub_78 : commonEnvelope childrenD_78 ⊆ insert (0, 0) required_78 := by decide |
| theorem child_required_sub_78 : ∀ j, childrenC_78 j ⊆ insert (0, 0) required_78 := by decide |
| theorem child_envelope_sub_78 : ∀ j, childrenD_78 j ⊆ envelope_78 := by decide |
| theorem pivot_mem_78 : (0, 0) ∈ envelope_78 := by decide |
| theorem children_work_78 : ∀ j, Template HasSnaky 2 (childrenC_78 j) (childrenD_78 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_6 4 (-1, 0)).mono (by decide) |
| · exact (placed_template_map row_works_52 0 (1, 0)).mono (by decide) |
| theorem row_works_78 : Template HasSnaky 3 required_78 envelope_78 := by |
| refine compose HasSnaky 2 childrenC_78 childrenD_78 children_work_78 (0, 0) |
| required_78 envelope_78 pivot_mem_78 child_required_sub_78 child_envelope_sub_78 ?_ |
| intro b hb; exact common_sub_78 (mem_commonEnvelope childrenD_78 b hb) |
| end SnakyConditional |
|
|
| end OAI |
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