Theorems · Theorem · general topology
Path.trans_symm
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y z : X} (γ : Path x y) (γ' : Path y z),
(γ.trans γ').symm = γ'.symm.trans γ.symm- Defined in
- Mathlib.Topology.Path
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 126 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- unitIntervalproof · cited by 607
- lt_of_not_geproof · cited by 374
- not_leproof · cited by 328
- Pathstatement and proof · cited by 318
- mul_subproof · cited by 201
Cited by3
Results whose statement or proof uses this declaration.
- curveIntegralFun_trans_of_half_ltproof · cited by 1
- Path.extend_trans_of_half_leproof · cited by 1
- Path.delayReflLeft_zeroproof · cited by 0