| import OAI.GameTheory.SnakyConditional.Templates.Level03Part01 |
| import OAI.GameTheory.SnakyConditional.Templates.Level03Part04 |
|
|
| namespace OAI |
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|
| namespace SnakyConditional |
| def required_17 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_17 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_17 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) required_0), (placedSet 0 (-1, -1) required_3)] |
| def childrenD_17 : Fin 2 → Finset Cell := ![(placedSet 6 (1, 0) envelope_0), (placedSet 0 (-1, -1) envelope_3)] |
| theorem common_sub_17 : commonEnvelope childrenD_17 ⊆ insert (0, 0) required_17 := by decide |
| theorem child_required_sub_17 : ∀ j, childrenC_17 j ⊆ insert (0, 0) required_17 := by decide |
| theorem child_envelope_sub_17 : ∀ j, childrenD_17 j ⊆ envelope_17 := by decide |
| theorem pivot_mem_17 : (0, 0) ∈ envelope_17 := by decide |
| theorem children_work_17 : ∀ j, Template HasSnaky 1 (childrenC_17 j) (childrenD_17 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_0 6 (1, 0)).mono (by decide) |
| · exact (placed_template_map row_works_3 0 (-1, -1)).mono (by decide) |
| theorem row_works_17 : Template HasSnaky 2 required_17 envelope_17 := by |
| refine compose HasSnaky 1 childrenC_17 childrenD_17 children_work_17 (0, 0) |
| required_17 envelope_17 pivot_mem_17 child_required_sub_17 child_envelope_sub_17 ?_ |
| intro b hb; exact common_sub_17 (mem_commonEnvelope childrenD_17 b hb) |
| def required_18 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_18 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_18 : Fin 2 → Finset Cell := ![(placedSet 6 (-2, 0) required_3), (placedSet 0 (0, -1) required_3)] |
| def childrenD_18 : Fin 2 → Finset Cell := ![(placedSet 6 (-2, 0) envelope_3), (placedSet 0 (0, -1) envelope_3)] |
| theorem common_sub_18 : commonEnvelope childrenD_18 ⊆ insert (0, 0) required_18 := by decide |
| theorem child_required_sub_18 : ∀ j, childrenC_18 j ⊆ insert (0, 0) required_18 := by decide |
| theorem child_envelope_sub_18 : ∀ j, childrenD_18 j ⊆ envelope_18 := by decide |
| theorem pivot_mem_18 : (0, 0) ∈ envelope_18 := by decide |
| theorem children_work_18 : ∀ j, Template HasSnaky 1 (childrenC_18 j) (childrenD_18 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_3 6 (-2, 0)).mono (by decide) |
| · exact (placed_template_map row_works_3 0 (0, -1)).mono (by decide) |
| theorem row_works_18 : Template HasSnaky 2 required_18 envelope_18 := by |
| refine compose HasSnaky 1 childrenC_18 childrenD_18 children_work_18 (0, 0) |
| required_18 envelope_18 pivot_mem_18 child_required_sub_18 child_envelope_sub_18 ?_ |
| intro b hb; exact common_sub_18 (mem_commonEnvelope childrenD_18 b hb) |
| end SnakyConditional |
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| end OAI |
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