Theorems · Theorem · linear algebra
neg_rayOfNeZero
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
[inst_3 : AddCommGroup M] [inst_4 : Module R M] (v : M) (h : v ≠ 0), -rayOfNeZero R v h = rayOfNeZero R (-v) ⋯The ray given by the negation of a nonzero vector.
- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- neg_ne_zerostatement · cited by 70
- Module.Raystatement · cited by 30
- rayOfNeZerostatement · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- Module.Ray.ne_neg_selfproof · cited by 3
- Module.Basis.orientation_eq_or_eq_negproof · cited by 2