Similar.exists_pos_pairwise_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],
Similar v₁ v₂ → ∃ r, 0 < r ∧ Pairwise fun i₁ i₂ => dist (v₁ i₁) (v₁ i₂) = r * dist (v₂ i₁) (v₂ i₂)Scales pairwise distance with positive ratio. Forward of
similar_iff_exists_pos_pairwise_dist_eq.
- Defined in
- Mathlib.Topology.MetricSpace.Similarity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Pairwisestatement · cited by 516
- Similarstatement · cited by 49
- similar_iff_exists_pos_pairwise_dist_eqproof · cited by 3
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