Theorems · Theorem · geometry

AffineSubspace.sOppSide_smul_vsub_vadd_left

∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P]
  {s : AffineSubspace R P} {x p₁ p₂ : P},
  x ∉ s → p₁ ∈ s → p₂ ∈ s → ∀ {t : R}, t < 0 → s.SOppSide (t • (x -ᵥ p₁) +ᵥ p₂) x

Defined in

Mathlib.Analysis.Convex.Side

Cited by

2 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor