Theorems · Theorem · linear algebra

Module.Ray.units_smul_of_neg

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] (u : Rˣ), ↑u < 0 → ∀ (v : Module.Ray R M), u • v = -v

Scaling by a negative unit is negation.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsStrictOrderedRingAddCommGroupModule