AffineSubspace.signedInfDist_eq_const_of_mem
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {s : AffineSubspace ℝ P} [inst_4 : Nonempty ↥s]
[inst_5 : s.direction.HasOrthogonalProjection] {p : P}, p ∈ s → ↑(s.signedInfDist p) = AffineMap.const ℝ P 0- Defined in
- Mathlib.Geometry.Euclidean.SignedDist
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement and proof · cited by 871
- VSub.vsubproof · cited by 817
- AffineMapstatement · cited by 674
- AffineSubspace.directionstatement and proof · cited by 339
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- vsub_selfproof · cited by 74
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