Similar.comm_left
∀ {P₁ : Type u_3} {P₂ : Type u_4} [inst : PseudoEMetricSpace P₁] [inst_1 : PseudoEMetricSpace P₂] {a b c : P₁}
{a' b' c' : P₂}, Similar ![a, b, c] ![a', b', c'] → Similar ![b, a, c] ![b', a', c']Swapping the first two vertices preserves similarity.
- Defined in
- Mathlib.Topology.MetricSpace.Similarity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Matrix.vecConsstatement and proof · cited by 852
- Matrix.vecEmptystatement and proof · cited by 832
- Equiv.swapproof · cited by 197
- Fintype.elemsproof · cited by 194
- Fintype.completeproof · cited by 192
- Similarstatement and proof · cited by 49
- Equiv.swap_apply_leftproof · cited by 44
- Equiv.swap_apply_of_ne_of_neproof · cited by 39
- Equiv.swap_apply_rightproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- Similar.reverse_of_threeproof · cited by 1
- EuclideanGeometry.similar_of_angle_angleproof · cited by 0
- Similar.angle_eq_allproof · cited by 0