Theorems · Theorem · general topology
IsometryEquiv.image_symm
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (h : α ≃ᵢ β),
Set.image ⇑h.symm = Set.preimage ⇑h- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 4 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- PseudoEMetricSpacestatement and proof · cited by 1,536
- IsometryEquivstatement and proof · cited by 177
- IsometryEquiv.symmstatement and proof · cited by 75
- Equiv.right_invproof · cited by 68
- Equiv.left_invproof · cited by 59
- IsometryEquiv.toEquivproof · cited by 33
- Set.image_eq_preimage_of_inverseproof · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- IsometryEquiv.dimH_preimageproof · cited by 1
- IsometryEquiv.ediam_preimageproof · cited by 0
- IsometryEquiv.diam_preimageproof · cited by 0
- IsometryEquiv.hausdorffMeasure_preimageproof · cited by 0