Theorems · Theorem · general topology

Isometry.piMap

∀ {ι : Type u_5} [inst : Fintype ι] {α : ι → Type u_3} {β : ι → Type u_4} [inst_1 : (i : ι) → PseudoEMetricSpace (α i)]
  [inst_2 : (i : ι) → PseudoEMetricSpace (β i)] (f : (i : ι) → α i → β i),
  (∀ (i : ι), Isometry (f i)) → Isometry (Pi.map f)

Defined in: Mathlib.Topology.MetricSpace.Isometry
Cited by: 0 results in Mathlib
Foundations: Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype PseudoEMetricSpace PseudoEMetricSpace

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

Fintypestatement and proof · cited by 7,736
Finset.univproof · cited by 3,473
PseudoEMetricSpacestatement and proof · cited by 1,536
EDist.edistproof · cited by 735
Finset.supproof · cited by 530
Isometrystatement and proof · cited by 230
Pi.mapstatement · cited by 60
Isometry.edist_eqproof · cited by 18

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