Theorems · Theorem · linear algebra
SameRay.zero_right
∀ {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 : M), SameRay R x 0- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- SameRaystatement · cited by 149
Cited by7
Results whose statement or proof uses this declaration.
- SameRay.sameRay_nonneg_smul_rightproof · cited by 6
- AffineSubspace.wOppSide_iff_exists_leftproof · cited by 5
- AffineSubspace.wSameSide_iff_exists_leftproof · cited by 5
- SameRay.transproof · cited by 4
- sameRay_iff_of_norm_eqproof · cited by 3
- sameRay_smul_smul_of_mul_nonnegproof · cited by 2
- SameRay.add_leftproof · cited by 2