Theorems · Theorem · group theory
right_ne_zero_of_smul
∀ {M : Type u_1} {A : Type u_7} [inst : Zero A] [inst_1 : SMulZeroClass M A] {a : M} {b : A}, a • b ≠ 0 → b ≠ 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- ZeroSMulZeroClass
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.
- SMulZeroClassstatement and proof · cited by 213
- smul_eq_zero_of_rightproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_smul_not_ltproof · cited by 2
- HahnSeries.SummableFamily.smul_support_subset_prodproof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumproof · cited by 2
- HahnSeries.order_smul_not_ltproof · cited by 1
- HahnSeries.SummableFamily.finite_co_support_prod_smulproof · cited by 1
- mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTopproof · cited by 0