Theorems · Theorem · linear algebra
SameRay.refl
∀ {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 xSameRay is reflexive.
- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- zero_lt_oneproof · cited by 598
- SameRaystatement · cited by 149
Cited by3
Results whose statement or proof uses this declaration.
- SameRay.rflproof · cited by 11
- Module.Basis.map_orientation_eq_det_inv_smulproof · cited by 3
- Orientation.eq_iff_norm_eq_and_oangle_eq_zeroproof · cited by 2