Theorems · Theorem · linear algebra
Module.Ray.neg_units_smul
∀ {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] (u : Rˣ) (v : Module.Ray R M), -u • v = -(u • v)- 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.
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
- Unitsstatement and proof · cited by 2,804
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Units.valproof · cited by 1,966
- neg_smulproof · cited by 306
- neg_ne_zeroproof · cited by 70
- Module.Raystatement and proof · cited by 30
- rayOfNeZeroproof · cited by 22
- smul_ne_zero_iff_neproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- units_smul_eq_neg_iffproof · cited by 2
- Module.Ray.units_smul_of_negproof · cited by 0