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Theorems · Theorem · general topology

Congruent.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], Congruent v₁ v₂ → ∀ (i₁ i₂ : ι), dist (v₁ i₁) (v₁ i₂) = dist (v₂ i₁) (v₂ i₂)

A congruence preserves distance. Forward direction of congruent_iff_dist_eq.

Defined in
Mathlib.Topology.MetricSpace.Congruence
Cited by
2 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoMetricSpacePseudoMetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

EuclideanGeometry.angle_eq_of_congruent · cited by 0EuclideanGeometry.angle_e…EuclideanGeometry.angle_angle_side · cited by 0EuclideanGeometry.angle_a…Real · cited by 25697RealPseudoMetricSpace · cited by 1550PseudoMetricSpaceDist.dist · cited by 1539Dist.distCongruent · cited by 37Congruentcongruent_iff_dist_eq · cited by 3congruent_iff_dist_eqCongruent.dist_eqCITED BYCITES

Cites5

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Cited by2

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