Theorems · Theorem · linear algebra

Module.Ray.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]
  (f : M ≃ₗ[R] N) (v : Module.Ray R M), (Module.Ray.map f) (-v) = -(Module.Ray.map f) v

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsStrictOrderedRingAddCommGroupAddCommGroupModuleModule