Theorems · Theorem · functional analysis
dist_eq_norm_vsub
∀ (V : Type u_2) {P : Type u_3} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
[inst_2 : NormedAddTorsor V P] (x y : P), dist x y = ‖x -ᵥ y‖The distance equals the norm of subtracting two points. In this
lemma, it is necessary to have V as an explicit argument; otherwise
rw dist_eq_norm_vsub sometimes doesn't work.
- Defined in
- Mathlib.Analysis.Normed.Group.AddTorsor
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- VSub.vsubstatement · cited by 817
- NormedAddTorsor.dist_eq_norm'proof · cited by 2
Cited by76
Results whose statement or proof uses this declaration.
- dist_eq_norm_vsub'proof · cited by 21
- dist_vadd_leftproof · cited by 9
- AffineIsometry.dist_mapproof · cited by 6
- dist_lineMap_lineMapproof · cited by 5
- Affine.Simplex.ExcenterExists.sign_touchpointWeightsproof · cited by 4
- Affine.Simplex.ExcenterExists.touchpoint_injectiveproof · cited by 4
- EuclideanGeometry.dist_smul_vadd_eq_distproof · cited by 4
- dist_vadd_cancel_rightproof · cited by 4
- EuclideanGeometry.inner_pos_or_eq_of_dist_le_radiusproof · cited by 3
- EuclideanGeometry.mul_dist_eq_abs_sub_sq_distproof · cited by 3
- EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_twoproof · cited by 3