Theorems · Theorem · general topology
Congruent.of_dist_eq
∀ {ι : Type u_1} {P₁ : Type u_3} {P₂ : Type u_4} {v₁ : ι → P₁} {v₂ : ι → P₂} [inst : PseudoMetricSpace P₁]
[inst_1 : PseudoMetricSpace P₂], (∀ (i₁ i₂ : ι), dist (v₁ i₁) (v₁ i₂) = dist (v₂ i₁) (v₂ i₂)) → Congruent v₁ v₂Congruence follows from preserved distance. Backward direction of congruent_iff_dist_eq.
- Defined in
- Mathlib.Topology.MetricSpace.Congruence
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Congruentstatement · cited by 37
- congruent_iff_dist_eqproof · cited by 3
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