Theorems · Theorem · ring theory
algebraMap.coe_mul
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (a b : R),
↑(a * b) = ↑a * ↑b- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- map_mulproof · cited by 1,137
- Algebra.caststatement · cited by 58
Cited by7
Results whose statement or proof uses this declaration.
- SameRay.sameRay_nonneg_smul_rightproof · cited by 6
- RCLike.ofReal_mulproof · cited by 3
- InnerProductSpace.Core.cauchy_schwarz_auxproof · cited by 1
- inner_eq_sum_norm_sq_div_fourproof · cited by 1
- PolynomialModule.eval_mapproof · cited by 1
- MeasureTheory.taylorWithinEval_charFun_zeroproof · cited by 1
- real_linearMap_map_smul_complexproof · cited by 0