Theorems · Theorem · algebraic topology
Path.Homotopic.hcomp
∀ {X : Type u} [inst : TopologicalSpace X] {x₀ x₁ x₂ : X} {p₀ p₁ : Path x₀ x₁} {q₀ q₁ : Path x₁ x₂},
p₀.Homotopic p₁ → q₀.Homotopic q₁ → (p₀.trans q₀).Homotopic (p₁.trans q₁)- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 130 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.
Cites6
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 and proof · cited by 28
- Nonempty.map2proof · cited by 8
- Path.Homotopy.hcompproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Path.Homotopic.Quotient.transproof · cited by 12
- Path.Homotopic.concat_twoproof · cited by 0