Theorems · Theorem · combinatorics
PreAbstractSimplicialComplex.isRelLowerSet_faces
∀ {ι : Type u_1} (self : PreAbstractSimplicialComplex ι), IsRelLowerSet self.faces Finset.NonemptyFaces are nonempty and downward closed: a non-empty subset of its spanning vertices spans another face.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 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.
- Finsetstatement · cited by 13,712
- Finset.Nonemptystatement · cited by 1,001
- PreAbstractSimplicialComplex.facesstatement · cited by 36
- IsRelLowerSetstatement · cited by 29
- PreAbstractSimplicialComplexstatement and proof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Geometry.SimplicialComplex.down_closedproof · cited by 3
- Geometry.SimplicialComplex.nonempty_of_mem_facesproof · cited by 1