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Theorems · Theorem · general topology

Congruent.index_map

∀ {ι : Type u_1} {ι' : Type u_2} {P₁ : Type u_3} {P₂ : Type u_4} {v₁ : ι → P₁} {v₂ : ι → P₂}
  [inst : PseudoEMetricSpace P₁] [inst_1 : PseudoEMetricSpace P₂],
  Congruent v₁ v₂ → ∀ (f : ι' → ι), Congruent (v₁ ∘ f) (v₂ ∘ f)

Change the index set ι to an index ι' that maps to ι.

Defined in
Mathlib.Topology.MetricSpace.Congruence
Cited by
1 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpace
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Congruent.index_equiv · cited by 0Congruent.index_equivPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceCongruent · cited by 37CongruentCongruent.edist_eq · cited by 2Congruent.edist_eqCongruent.index_mapCITED BYCITES

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