Theorems · Theorem · general topology
OpenPartialHomeomorph.left_inv
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y) {x : X}, x ∈ e.source → ↑e.symm (↑e x) = x- Cited by
- 78 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- PartialEquiv.sourcestatement and proof · cited by 964
- PartialHomeomorph.toPartialEquivstatement and proof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement and proof · cited by 851
- OpenPartialHomeomorph.toFun'statement · cited by 745
- OpenPartialHomeomorphstatement and proof · cited by 664
- OpenPartialHomeomorph.symmstatement · cited by 460
- PartialEquiv.left_inv'proof · cited by 6
Cited by78
Results whose statement or proof uses this declaration.
- ContMDiffWithinAt.compproof · cited by 18
- differentiableWithinAt_localInvariantPropproof · cited by 13
- HasMFDerivWithinAt.compproof · cited by 7
- OpenPartialHomeomorph.leftInvOnproof · cited by 5
- Filter.EventuallyEq.mfderivWithin_eqproof · cited by 5
- OpenPartialHomeomorph.map_nhdsWithin_eqproof · cited by 4
- Filter.EventuallyEq.mlieBracketWithin_vectorField_eqproof · cited by 4
- HasMFDerivWithinAt.congr_of_eventuallyEqproof · cited by 4
- OpenPartialHomeomorph.tendsto_symmproof · cited by 4
- VectorField.mlieBracketWithin_smul_rightproof · cited by 3
- ContMDiffWithinAt.mfderivWithinproof · cited by 3
- ContMDiffWithinAt.mlieBracketWithin_vectorFieldproof · cited by 3