Theorems · Theorem · linear algebra

Module.Basis.orientation_eq_or_eq_neg

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] {ι : Type u_3} [inst_5 : Fintype ι] [inst_6 : DecidableEq ι]
  (e : Module.Basis ι R M) (x : Orientation R M ι), x = e.orientation ∨ x = -e.orientation

Given a basis, any orientation equals the orientation given by that basis or its negation.

Defined in

Mathlib.LinearAlgebra.Orientation

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingAddCommGroupModuleFintypeDecidableEq