Theorems · Theorem · linear algebra

SameRay.add_left

∀ {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] {x y z : M}, SameRay R x z → SameRay R y z → SameRay R (x + y) z

If x and y are on the same ray as z, then so is x + y.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule