Theorems · Theorem · linear algebra

Orientation.map_neg

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  {N : Type u_3} [inst_3 : AddCommGroup M] [inst_4 : AddCommGroup N] [inst_5 : Module R M] [inst_6 : Module R N]
  {ι : Type u_4} (f : M ≃ₗ[R] N) (x : Orientation R M ι), (Orientation.map ι f) (-x) = -(Orientation.map ι f) x

Defined in

Mathlib.LinearAlgebra.Orientation

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsStrictOrderedRingAddCommGroupAddCommGroupModuleModule