Theorems · Theorem · group theory
smul_add
∀ {M : Type u_1} {A : Type u_7} [inst : AddZeroClass A] [inst_1 : DistribSMul M A] (a : M) (b₁ b₂ : A),
a • (b₁ + b₂) = a • b₁ + a • b₂- Cited by
- 263 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 22 definitions · uses no axioms
- Assumes
- AddZeroClassDistribSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddZeroClassstatement and proof · cited by 1,237
- DistribSMulstatement and proof · cited by 117
- DistribSMul.smul_addproof · cited by 1
Cited by263
Results whose statement or proof uses this declaration.
- smul_negproof · cited by 181
- smul_subproof · cited by 142
- Submodule.mem_supproof · cited by 73
- realPart_apply_coeproof · cited by 9
- MeromorphicAt.addproof · cited by 8
- intervalIntegral.integral_addproof · cited by 7
- Algebra.IsPushout.symmproof · cited by 7
- Real.circleAverage_addproof · cited by 6
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- CochainComplex.HomComplex.δ_compproof · cited by 5
- isBoundedBilinearMap_smulproof · cited by 5
- IsBaseChange.of_lift_uniqueproof · cited by 5
Showing the 200 most cited of 263.