Theorems · Theorem · group theory
left_ne_zero_of_smul
∀ {M₀ : Type u_2} {A : Type u_7} [inst : Zero M₀] [inst_1 : Zero A] [inst_2 : SMulWithZero M₀ A] {a : M₀} {b : A},
a • b ≠ 0 → a ≠ 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- ZeroZeroSMulWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SMulWithZerostatement and proof · cited by 113
- smul_eq_zero_of_leftproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.smul_support_subset_prodproof · cited by 2
- exists_contMDiffSection_forall_mem_convex_of_localproof · cited by 1
- IsVisible.mem_convexHull_isVisibleproof · cited by 1
- HahnSeries.SummableFamily.finite_co_support_prod_smulproof · cited by 1