Theorems · Theorem · ring theory
AddMonoidAlgebra.mapDomain_mul
∀ {F : Type u_2} {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] [inst_1 : Add M] [inst_2 : Add N]
[inst_3 : FunLike F M N] [AddHomClass F M N] (f : F) (x y : AddMonoidAlgebra R M),
AddMonoidAlgebra.mapDomain (⇑f) (x * y) = AddMonoidAlgebra.mapDomain (⇑f) x * AddMonoidAlgebra.mapDomain (⇑f) y- Defined in
- Mathlib.Algebra.MonoidAlgebra.MapDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- FunLikestatement and proof · cited by 2,560
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- map_addproof · cited by 964
- AddMonoidAlgebrastatement and proof · cited by 649
- Finsupp.sumproof · cited by 481
- mul_addproof · cited by 413
- AddMonoidAlgebra.coeffproof · cited by 365
- add_mulproof · cited by 363
- AddMonoidAlgebra.singleproof · cited by 250
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