Theorems · Theorem · group theory
smul_zero
∀ {M : Type u_1} {A : Type u_7} [inst : Zero A] [inst_1 : SMulZeroClass M A] (a : M), a • 0 = 0- Cited by
- 665 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 15 definitions · 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
- SMulZeroClass.smul_zeroproof · cited by 1
Cited by665
Results whose statement or proof uses this declaration.
- smul_negproof · cited by 181
- MeasureTheory.integral_constproof · cited by 75
- Submodule.span_zero_singletonproof · cited by 26
- norm_smul_leproof · cited by 24
- MeasureTheory.Measure.map_smulproof · cited by 21
- smul_nonnegproof · cited by 21
- meromorphicOrderAt_eq_top_iffproof · cited by 20
- integral_smul_constproof · cited by 17
- MeasureTheory.tilted_zero_measureproof · cited by 12
- Derivation.map_algebraMapproof · cited by 12
- MultilinearMap.map_coord_zeroproof · cited by 12
- FractionalIdeal.spanSingleton_zeroproof · cited by 11
Showing the 200 most cited of 665.