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Theorems · Theorem · general topology

IsometryEquiv.symm_apply_eq

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

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

IsometryEquiv.midpoint_fixed · cited by 1IsometryEquiv.midpoint_fi…IsometryEquiv.map_midpoint · cited by 0IsometryEquiv.map_midpointDFunLike.coe · cited by 62936DFunLike.coePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceIsometryEquiv · cited by 177IsometryEquivIsometryEquiv.symm · cited by 75IsometryEquiv.symmEquiv.symm_apply_eq · cited by 63Equiv.symm_apply_eqIsometryEquiv.toEquiv · cited by 33IsometryEquiv.toEquivIsometryEquiv.symm_apply_eqCITED BYCITES

Cites6

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Cited by2

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