EuclideanGeometry.triangle_congruent_iff_dist_eq
∀ {P₁ : Type u_4} {P₂ : Type u_5} [inst : MetricSpace P₁] [inst_1 : MetricSpace P₂] {t₁ : Fin 3 → P₁} {t₂ : Fin 3 → P₂},
Congruent t₁ t₂ ↔ ∀ (i j : Fin 3), dist (t₁ i) (t₁ j) = dist (t₂ i) (t₂ j)- Defined in
- Mathlib.Geometry.Euclidean.Congruence
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- Congruentstatement · cited by 37
- congruent_iff_dist_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.side_side_sideproof · cited by 1