Theorems · Definition · category theory
ComplexShape.Embedding.BoundaryLE
{ι : Type u_1} → {ι' : Type u_2} → {c : ComplexShape ι} → {c' : ComplexShape ι'} → c.Embedding c' → ι → PropThe upper boundary of an embedding e : Embedding c c', as a predicate on ι.
It is satisfied by j : ι when there exists k' : ι' not in the image of e.f
such that c'.Rel (e.f j) k'.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ComplexShapestatement and proof · cited by 1,684
- ComplexShape.Relproof · cited by 518
- ComplexShape.Embeddingstatement and proof · cited by 337
- ComplexShape.nextproof · cited by 297
- ComplexShape.Embedding.fproof · cited by 251
Cited by26
Results whose statement or proof uses this declaration.
- HomologicalComplex.truncLE'XIsostatement and proof · cited by 4
- ComplexShape.Embedding.not_boundaryLE_prevstatement · cited by 3
- HomologicalComplex.truncLE'XIsoCyclesstatement and proof · cited by 2
- ComplexShape.Embedding.AreComplementary.Boundary.exists₁statement and proof · cited by 1
- ComplexShape.Embedding.AreComplementary.Boundary.indexOfBoundaryLEstatement and proof · cited by 1
- ComplexShape.Embedding.boundaryLEstatement · cited by 1
- HomologicalComplex.truncLE'Map_f_eqstatement and proof · cited by 0
- HomologicalComplex.truncLE'Map_f_eq_cyclesMapstatement and proof · cited by 0
- HomologicalComplex.truncLE'_d_eqstatement and proof · cited by 0
- HomologicalComplex.truncLE'_d_eq_toCyclesstatement and proof · cited by 0
- HomologicalComplex.truncLEXIsostatement and proof · cited by 0
- HomologicalComplex.truncLEXIsoCyclesstatement and proof · cited by 0