Theorems · Theorem · algebraic topology
Path.Homotopic.Quotient.eq
∀ {X : Type u} [inst : TopologicalSpace X] {x₀ x₁ : X} {p q : Path x₀ x₁},
Path.Homotopic.Quotient.mk p = Path.Homotopic.Quotient.mk q ↔ p.Homotopic q- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 133 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.Homotopic.Quotientstatement · cited by 55
- Quotient.eqproof · cited by 50
- Path.Homotopicstatement · cited by 28
- Path.Homotopic.Quotient.mkstatement · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- simply_connected_iff_loops_nullhomotopicproof · cited by 1
- IsCoveringMap.injective_path_homotopic_mapproof · cited by 0
- IsCoveringMap.existsUnique_continuousMap_lifts_of_range_leproof · cited by 0