Theorems · Theorem · linear algebra

Module.Ray.units_smul_of_pos

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

Scaling by a positive unit is a no-op.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule