Affine.Simplex.altitudeFoot_mem_altitude
∀ {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] {n : ℕ} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
s.altitudeFoot i ∈ s.altitude i- Defined in
- Mathlib.Geometry.Euclidean.Altitude
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.pointsproof · cited by 391
- Affine.Simplex.altitudeFootstatement and proof · cited by 23
- Affine.Simplex.altitudestatement · cited by 17
- left_mem_affineSpan_pairproof · cited by 15
- Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitudeproof · cited by 1
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