Mathlib Map

Theorems · Theorem · general topology

IsometryEquiv.eq_symm_apply

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (h : α ≃ᵢ β) {x : α} {y : β},
  x = h.symm y ↔ h x = y
Defined in
Mathlib.Topology.MetricSpace.Isometry
Cited by
1 results in Mathlib
Foundations
Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsometryEquiv.map_midpoint · cited by 0IsometryEquiv.map_midpointDFunLike.coe · cited by 62936DFunLike.coePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceIsometryEquiv · cited by 177IsometryEquivEquiv.eq_symm_apply · cited by 85Equiv.eq_symm_applyIsometryEquiv.symm · cited by 75IsometryEquiv.symmIsometryEquiv.toEquiv · cited by 33IsometryEquiv.toEquivIsometryEquiv.eq_symm_applyCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.