Theorems · Theorem · linear algebra
units_inv_smul
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : LinearOrder 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⁻¹ • v = u • vScaling by an inverse unit is the same as scaling by itself.
- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- LinearOrderstatement and proof · cited by 8,572
- Unitsstatement and proof · cited by 2,804
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Units.valproof · cited by 1,966
- SemigroupAction.mul_smulproof · cited by 291
- Units.ne_zeroproof · cited by 68
- smul_inv_smulproof · cited by 53
- Module.Raystatement and proof · cited by 30
- mul_self_posproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Orientation.map_eq_iff_det_posproof · cited by 3
- Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negproof · cited by 0
- Module.Basis.orientation_comp_linearEquiv_eq_iff_det_posproof · cited by 0
- Orientation.map_eq_neg_iff_det_negproof · cited by 0