Theorems · Theorem · linear algebra
Module.Ray.ne_neg_self
∀ {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] [IsDomain R] [Module.IsTorsionFree R M] (x : Module.Ray R M), x ≠ -xA ray does not equal its own negation.
- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- IsDomainstatement and proof · cited by 2,196
- Module.IsTorsionFreestatement and proof · cited by 600
- neg_ne_zeroproof · cited by 70
- Module.Raystatement and proof · cited by 30
- rayOfNeZeroproof · cited by 22
- Module.Ray.indproof · cited by 10
- ray_eq_iffproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.orientation_ne_iff_eq_negproof · cited by 2
- Orientation.ne_iff_eq_negproof · cited by 0
- Orientation.map_eq_neg_iff_det_negproof · cited by 0