Mathlib Map

Theorems · Theorem · general topology

DilationEquiv.apply_symm_apply

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] (e : X ≃ᵈ Y) (x : Y),
  e (e.symm x) = x
Defined in
Mathlib.Topology.MetricSpace.DilationEquiv
Cited by
1 results in Mathlib
Foundations
Depth 155 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.

DilationEquiv.symm_trans_self · cited by 1DilationEquiv.symm_trans_…DFunLike.coe · cited by 62936DFunLike.coePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEquiv.right_inv · cited by 68Equiv.right_invDilationEquiv · cited by 55DilationEquivDilationEquiv.symm · cited by 19DilationEquiv.symmDilationEquiv.toEquiv · cited by 10DilationEquiv.toEquivDilationEquiv.apply_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.