Theorems · Theorem · functional analysis
dist_vadd_left
∀ {V : Type u_2} {P : Type u_3} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
[inst_2 : NormedAddTorsor V P] (v : V) (x : P), dist (v +ᵥ x) x = ‖v‖- Defined in
- Mathlib.Analysis.Normed.Group.AddTorsor
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HVAdd.hVAddstatement and proof · cited by 1,820
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- dist_eq_norm_vsubproof · cited by 76
- vadd_vsubproof · cited by 58
Cited by9
Results whose statement or proof uses this declaration.
- EuclideanGeometry.dist_inversion_centerproof · cited by 5
- dist_vadd_rightproof · cited by 2
- AffineSpace.asymptoticNhds_le_coboundedproof · cited by 2
- dist_affineCombination_lt_of_strictConvexSpaceproof · cited by 1
- EuclideanGeometry.Sphere.nonempty_iffproof · cited by 1
- IsOpen.exists_between_affineIndependent_span_eq_topproof · cited by 1
- EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_iffproof · cited by 0
- nndist_vadd_leftproof · cited by 0
- DilationEquiv.smulTorsor_preimage_ballproof · cited by 0