Theorems · Theorem · linear algebra
SameRay.rfl
∀ {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 x- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 27 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
- SameRaystatement · cited by 149
- SameRay.reflproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- sameRay_iff_of_norm_eqproof · cited by 3
- IsMaxFilter.norm_add_selfproof · cited by 3
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- Complex.eqOn_of_isPreconnected_of_isMaxOn_normproof · cited by 2
- lt_norm_sub_of_not_sameRayproof · cited by 2
- AffineSubspace.wOppSide_self_iffproof · cited by 1
- AffineSubspace.wSameSide_self_iffproof · cited by 1
- Module.Basis.orientation_unitsSMulproof · cited by 1
- Complex.eq_of_isMaxOn_of_ball_subsetproof · cited by 1
- MDifferentiableOn.eqOn_of_isPreconnected_of_isMaxOn_normproof · cited by 0