Similar.of_exists_nndist_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],
(∃ r, r ≠ 0 ∧ ∀ (i₁ i₂ : ι), nndist (v₁ i₁) (v₁ i₂) = r * nndist (v₂ i₁) (v₂ i₂)) → Similar v₁ v₂Similarity follows from scaled non-negative distance. Backward direction of
similar_iff_exists_nndist_eq.
- Defined in
- Mathlib.Topology.MetricSpace.Similarity
- 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.
- NNRealstatement · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- NNDist.nndiststatement · cited by 235
- Similarstatement · cited by 49
- similar_iff_exists_nndist_eqproof · cited by 3
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