Theorems · Theorem · algebraic topology
Path.Homotopic.trans_assoc
∀ {X : Type u_1} [inst : TopologicalSpace X] {x₀ x₁ x₂ x₃ : X} (p : Path x₀ x₁) (q : Path x₁ x₂) (r : Path x₂ x₃),
((p.trans q).trans r).Homotopic (p.trans (q.trans r))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Pathstatement and proof · cited by 318
- Path.transstatement · cited by 54
- Path.Homotopicstatement · cited by 28
- Path.Homotopy.transAssocproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Path.Homotopic.Quotient.trans_assocproof · cited by 1