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Theorems · Theorem · algebraic topology

SSet.Path.ext

∀ {X : SSet} {n : ℕ} {f g : X.Path n}, f.vertex = g.vertex → f.arrow = g.arrow → f = g
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Path
Cited by
2 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.Path.ext₀ · cited by 2Path.ext₀SSet.Path.ext_iff · cited by 0Path.ext_iffCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategorySSet · cited by 1283SSetSSet.Path · cited by 46SSet.PathSSet.Path.arrow · cited by 27Path.arrowSSet.Path.vertex · cited by 19Path.vertexSSet.Truncated.Path.ext · cited by 4Path.extPath.extCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.