Theorems · Definition · general topology
Congruent
{ι : Type u_1} →
{P₁ : Type u_3} → {P₂ : Type u_4} → [PseudoEMetricSpace P₁] → [PseudoEMetricSpace P₂] → (ι → P₁) → (ι → P₂) → PropA congruence between indexed sets of vertices v₁ and v₂.
Use open scoped Congruent to access the v₁ ≅ v₂ notation.
- Defined in
- Mathlib.Topology.MetricSpace.Congruence
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
Cited by37
Results whose statement or proof uses this declaration.
- Congruent.transstatement and proof · cited by 3
- congruent_iff_dist_eqstatement · cited by 3
- congruent_iff_nndist_eqstatement · cited by 3
- Congruent.dist_eqstatement · cited by 2
- Congruent.edist_eqstatement · cited by 2
- Congruent.symmstatement and proof · cited by 2
- congruent_iff_edist_eqstatement · cited by 2
- congruent_iff_pairwise_dist_eqstatement · cited by 2
- congruent_iff_pairwise_edist_eqstatement and proof · cited by 2
- congruent_iff_pairwise_nndist_eqstatement · cited by 2
- EuclideanGeometry.angle_side_anglestatement · cited by 1
- Congruent.comp_leftstatement and proof · cited by 1