| import OAI.GameTheory.SnakyConditional.Templates.Level03Part05 |
| import OAI.GameTheory.SnakyConditional.Templates.Level04Part01 |
| import OAI.GameTheory.SnakyConditional.Templates.Level04Part02 |
| import OAI.GameTheory.SnakyConditional.Templates.Level04Part04 |
|
|
| namespace OAI |
|
|
| namespace SnakyConditional |
| def required_19 : Finset Cell := ⟨(([(-2, 0), (-2, 1), (-1, 0), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_19 : Finset Cell := ⟨(([(-3, 1), (-2, 0), (-2, 1), (-1, 0), (0, 0), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_19 : Fin 2 → Finset Cell := ![(placedSet 4 (-3, 1) required_6), (placedSet 0 (2, 1) required_6)] |
| def childrenD_19 : Fin 2 → Finset Cell := ![(placedSet 4 (-3, 1) envelope_6), (placedSet 0 (2, 1) envelope_6)] |
| theorem common_sub_19 : commonEnvelope childrenD_19 ⊆ insert (0, 0) required_19 := by decide |
| theorem child_required_sub_19 : ∀ j, childrenC_19 j ⊆ insert (0, 0) required_19 := by decide |
| theorem child_envelope_sub_19 : ∀ j, childrenD_19 j ⊆ envelope_19 := by decide |
| theorem pivot_mem_19 : (0, 0) ∈ envelope_19 := by decide |
| theorem children_work_19 : ∀ j, Template HasSnaky 2 (childrenC_19 j) (childrenD_19 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_6 4 (-3, 1)).mono (by decide) |
| · exact (placed_template_map row_works_6 0 (2, 1)).mono (by decide) |
| theorem row_works_19 : Template HasSnaky 3 required_19 envelope_19 := by |
| refine compose HasSnaky 2 childrenC_19 childrenD_19 children_work_19 (0, 0) |
| required_19 envelope_19 pivot_mem_19 child_required_sub_19 child_envelope_sub_19 ?_ |
| intro b hb |
| def required_20 : Finset Cell := ⟨(([(-3, 0), (-3, 1), (-2, 0), (-1, 0), (0, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_20 : Finset Cell := ⟨(([(-4, 1), (-3, 0), (-3, 1), (-2, 0), (-1, 0), (0, 0), (0, 1), (1, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_20 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) required_6), (placedSet 0 (1, 1) required_6)] |
| def childrenD_20 : Fin 2 → Finset Cell := ![(placedSet 4 (-4, 1) envelope_6), (placedSet 0 (1, 1) envelope_6)] |
| theorem common_sub_20 : commonEnvelope childrenD_20 ⊆ insert (0, 0) required_20 := by decide |
| theorem child_required_sub_20 : ∀ j, childrenC_20 j ⊆ insert (0, 0) required_20 := by decide |
| theorem child_envelope_sub_20 : ∀ j, childrenD_20 j ⊆ envelope_20 := by decide |
| theorem pivot_mem_20 : (0, 0) ∈ envelope_20 := by decide |
| theorem children_work_20 : ∀ j, Template HasSnaky 2 (childrenC_20 j) (childrenD_20 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_6 4 (-4, 1)).mono (by decide) |
| · exact (placed_template_map row_works_6 0 (1, 1)).mono (by decide) |
| theorem row_works_20 : Template HasSnaky 3 required_20 envelope_20 := by |
| refine compose HasSnaky 2 childrenC_20 childrenD_20 children_work_20 (0, 0) |
| required_20 envelope_20 pivot_mem_20 child_required_sub_20 child_envelope_sub_20 ?_ |
| intro b hb |
| def required_21 : Finset Cell := ⟨(([(-3, -1), (-2, 0), (-1, 0), (1, 0), (1, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_21 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-2, 0), (-1, 0), (0, 0), (1, 0), (1, 1), (2, 1)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_21 : Fin 2 → Finset Cell := ![(placedSet 6 (-2, -1) required_4), (placedSet 0 (2, 1) required_6)] |
| def childrenD_21 : Fin 2 → Finset Cell := ![(placedSet 6 (-2, -1) envelope_4), (placedSet 0 (2, 1) envelope_6)] |
| theorem common_sub_21 : commonEnvelope childrenD_21 ⊆ insert (0, 0) required_21 := by decide |
| theorem child_required_sub_21 : ∀ j, childrenC_21 j ⊆ insert (0, 0) required_21 := by decide |
| theorem child_envelope_sub_21 : ∀ j, childrenD_21 j ⊆ envelope_21 := by decide |
| theorem pivot_mem_21 : (0, 0) ∈ envelope_21 := by decide |
| theorem children_work_21 : ∀ j, Template HasSnaky 2 (childrenC_21 j) (childrenD_21 j) := by |
| intro j |
| fin_cases j |
| · exact (placed_template_map row_works_4 6 (-2, -1)).mono (by decide) |
| · exact (placed_template_map row_works_6 0 (2, 1)).mono (by decide) |
| theorem row_works_21 : Template HasSnaky 3 required_21 envelope_21 := by |
| refine compose HasSnaky 2 childrenC_21 childrenD_21 children_work_21 (0, 0) |
| required_21 envelope_21 pivot_mem_21 child_required_sub_21 child_envelope_sub_21 ?_ |
| intro b hb |
| def required_24 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_24 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-1, -1), (-1, 0), (0, -1), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_24 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) required_0), (placedSet 0 (1, 0) required_17)] |
| def childrenD_24 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) envelope_0), (placedSet 0 (1, 0) envelope_17)] |
| theorem common_sub_24 : commonEnvelope childrenD_24 ⊆ insert (0, 0) required_24 := by decide |
| theorem child_required_sub_24 : ∀ j, childrenC_24 j ⊆ insert (0, 0) required_24 := by decide |
| theorem child_envelope_sub_24 : ∀ j, childrenD_24 j ⊆ envelope_24 := by decide |
| theorem pivot_mem_24 : (0, 0) ∈ envelope_24 := by decide |
| theorem children_work_24 : ∀ j, Template HasSnaky 2 (childrenC_24 j) (childrenD_24 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_17 0 (1, 0)).mono (by decide) |
| theorem row_works_24 : Template HasSnaky 3 required_24 envelope_24 := by |
| refine compose HasSnaky 2 childrenC_24 childrenD_24 children_work_24 (0, 0) |
| required_24 envelope_24 pivot_mem_24 child_required_sub_24 child_envelope_sub_24 ?_ |
| intro b hb |
| def required_25 : Finset Cell := ⟨(([(-3, -1), (-2, -1), (-1, -1), (-1, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def envelope_25 : Finset Cell := ⟨(([(-4, -1), (-3, -1), (-2, -1), (-2, 0), (-1, -1), (-1, 0), (0, 0), (1, 0), (2, 0)] : List Cell) : Multiset Cell), by decide⟩ |
| def childrenC_25 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) required_0), (placedSet 0 (1, 0) required_14)] |
| def childrenD_25 : Fin 2 → Finset Cell := ![(placedSet 0 (-4, -1) envelope_0), (placedSet 0 (1, 0) envelope_14)] |
| theorem common_sub_25 : commonEnvelope childrenD_25 ⊆ insert (0, 0) required_25 := by decide |
| theorem child_required_sub_25 : ∀ j, childrenC_25 j ⊆ insert (0, 0) required_25 := by decide |
| theorem child_envelope_sub_25 : ∀ j, childrenD_25 j ⊆ envelope_25 := by decide |
| theorem pivot_mem_25 : (0, 0) ∈ envelope_25 := by decide |
| theorem children_work_25 : ∀ j, Template HasSnaky 2 (childrenC_25 j) (childrenD_25 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_14 0 (1, 0)).mono (by decide) |
| theorem row_works_25 : Template HasSnaky 3 required_25 envelope_25 := by |
| refine compose HasSnaky 2 childrenC_25 childrenD_25 children_work_25 (0, 0) |
| required_25 envelope_25 pivot_mem_25 child_required_sub_25 child_envelope_sub_25 ?_ |
| intro b hb |
| end SnakyConditional |
|
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| end OAI |
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