Theorems · Theorem · linear algebra

sameRay_of_mem_orbit

∀ {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] {v₁ v₂ : M},
  v₁ ∈ MulAction.orbit (↥(Units.posSubgroup R)) v₂ → SameRay R v₁ v₂

SameRay follows from membership of MulAction.orbit for the Units.posSubgroup.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingAddCommGroupModule