Theorems · Theorem · general topology
IsometryEquiv.apply_symm_apply
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (h : α ≃ᵢ β) (y : β),
h (h.symm y) = y- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Equiv.apply_symm_applyproof · cited by 346
- IsometryEquivstatement and proof · cited by 177
- IsometryEquiv.symmstatement · cited by 75
- IsometryEquiv.toEquivproof · cited by 33
Cited by7
Results whose statement or proof uses this declaration.
- IsometryEquiv.preimage_ballproof · cited by 4
- IsometryEquiv.preimage_closedBallproof · cited by 4
- IsometryEquiv.preimage_sphereproof · cited by 4
- IsometryEquiv.preimage_closedEBallproof · cited by 2
- IsometryEquiv.preimage_eballproof · cited by 2
- IsometryEquiv.midpoint_fixedproof · cited by 1
- IsometryEquiv.apply_inv_selfproof · cited by 0