Theorems · Theorem · general topology
Congruent.of_edist_eq
∀ {ι : Type u_1} {P₁ : Type u_3} {P₂ : Type u_4} {v₁ : ι → P₁} {v₂ : ι → P₂} [inst : PseudoEMetricSpace P₁]
[inst_1 : PseudoEMetricSpace P₂], (∀ (i₁ i₂ : ι), edist (v₁ i₁) (v₁ i₂) = edist (v₂ i₁) (v₂ i₂)) → Congruent v₁ v₂Congruence follows from preserved extended distance. Backward direction of
congruent_iff_edist_eq.
- Defined in
- Mathlib.Topology.MetricSpace.Congruence
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement · cited by 735
- Congruentstatement · cited by 37
- congruent_iff_edist_eqproof · cited by 2
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