Theorems · Theorem · geometry

AffineSubspace.wOppSide_iff_exists_right

∀ {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 p₂ : P}, p₂ ∈ s → (s.WOppSide x y ↔ y ∈ s ∨ ∃ p₁ ∈ s, SameRay R (x -ᵥ p₁) (p₂ -ᵥ y))

Defined in

Mathlib.Analysis.Convex.Side

Cited by

1 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor