Theorems · Theorem · linear algebra
smul_rayOfNeZero
∀ {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] {G : Type u_5} [inst_5 : Group G] [inst_6 : DistribMulAction G M]
[inst_7 : SMulCommClass R G M] (g : G) (v : M) (hv : v ≠ 0), g • rayOfNeZero R v hv = rayOfNeZero R (g • v) ⋯- Defined in
- Mathlib.LinearAlgebra.Ray
- Cited by
- 3 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.
Cites11
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
- Groupstatement and proof · cited by 6,238
- IsStrictOrderedRingstatement and proof · cited by 2,490
- SMulCommClassstatement and proof · cited by 1,927
- DistribMulActionstatement and proof · cited by 584
- Module.Raystatement · cited by 30
- rayOfNeZerostatement · cited by 22
- smul_ne_zero_iff_nestatement · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.map_orientation_eq_det_inv_smulproof · cited by 3
- Module.Ray.units_smul_of_posproof · cited by 2
- Module.Basis.orientation_unitsSMulproof · cited by 1