Theorems · Theorem · geometry

AffineSubspace.wSameSide_iff_exists_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 y p₁ : P}, p₁ ∈ s → (s.WSameSide x y ↔ x ∈ s ∨ ∃ p₂ ∈ s, SameRay R (x -ᵥ p₁) (y -ᵥ p₂))

Defined in

Mathlib.Analysis.Convex.Side

Cited by

5 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor