Theorems · Inductive type · category theory
ComplexShape.Embedding.AreComplementary
{ι : Type u_1} →
{ι₁ : Type u_2} →
{ι₂ : Type u_3} →
{c : ComplexShape ι} → {c₁ : ComplexShape ι₁} → {c₂ : ComplexShape ι₂} → c₁.Embedding c → c₂.Embedding c → PropTwo embedding e₁ and e₂ into a complex shape c : ComplexShape ι
are complementary when the range of e₁.f and e₂.f form a partition of ι.
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ComplexShapestatement · cited by 1,684
- ComplexShape.Embeddingstatement · cited by 337
Cited by42
Results whose statement or proof uses this declaration.
- ComplexShape.Embedding.AreComplementary.Boundarystatement and proof · cited by 9
- ComplexShape.Embedding.AreComplementary.equivstatement and proof · cited by 7
- ComplexShape.Embedding.AreComplementary.disjointstatement and proof · cited by 6
- ComplexShape.Embedding.AreComplementary.exists_i₁statement and proof · cited by 4
- ComplexShape.Embedding.AreComplementary.symmstatement and proof · cited by 4
- ComplexShape.Embedding.AreComplementary.unionstatement and proof · cited by 4
- HomologicalComplex.shortComplexTruncLEX₃ToTruncGEstatement and proof · cited by 3
- ComplexShape.Embedding.embeddingUpInt_areComplementarystatement · cited by 3
- HomologicalComplex.g_shortComplexTruncLEX₃ToTruncGEstatement and proof · cited by 2
- ComplexShape.Embedding.AreComplementary.descstatement and proof · cited by 2
- ComplexShape.Embedding.AreComplementary.desc'statement and proof · cited by 2
- ComplexShape.Embedding.AreComplementary.isStrictlySupportedOutside₁_iffstatement and proof · cited by 2