Theorems · Theorem · functional analysis
dist_lineMap_left
∀ {V : Type u_1} {P : Type u_2} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
[inst_2 : NormedAddTorsor V P] {𝕜 : Type u_5} [inst_3 : NormedField 𝕜] [inst_4 : NormedSpace 𝕜 V] (p₁ p₂ : P) (c : 𝕜),
dist ((AffineMap.lineMap p₁ p₂) c) p₁ = ‖c‖ * dist p₁ p₂- Defined in
- Mathlib.Analysis.Normed.Affine.AddTorsor
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- NormedFieldstatement and proof · cited by 1,084
- AffineMapstatement · cited by 674
- AffineMap.lineMapstatement and proof · cited by 254
- dist_zero_rightproof · cited by 172
Cited by7
Results whose statement or proof uses this declaration.
- dist_left_midpointproof · cited by 7
- dist_left_lineMapproof · cited by 3
- Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleOproof · cited by 1
- EuclideanGeometry.Sphere.isIntTangent_iff_dist_centerproof · cited by 0
- EuclideanGeometry.Sphere.isExtTangent_iff_dist_centerproof · cited by 0
- nndist_lineMap_leftproof · cited by 0