Theorems · Theorem · general topology
Path.map_trans
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x y z : X} (γ : Path x y)
(γ' : Path y z) {f : X → Y} (h : Continuous f), (γ.trans γ').map h = (γ.map h).trans (γ'.map h)- Defined in
- Mathlib.Topology.Path
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- Continuousstatement and proof · cited by 2,592
- LT.lt.leproof · cited by 2,189
- unitIntervalproof · cited by 607
- not_leproof · cited by 328
- Pathstatement and proof · cited by 318
- zero_lt_twoproof · cited by 124
- Path.transstatement and proof · cited by 54
- Path.extproof · cited by 30
- Path.mapstatement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- IsCoveringMap.existsUnique_continuousMap_lifts_of_range_leproof · cited by 0