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Theorems · Theorem · ring theory

AddMonoidAlgebra.coeff_mapDomain

∀ {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] (f : M → N) (x : AddMonoidAlgebra R M),
  (AddMonoidAlgebra.mapDomain f x).coeff = Finsupp.mapDomain f x.coeff
Defined in
Mathlib.Algebra.MonoidAlgebra.MapDomain
Cited by
9 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddMonoidAlgebra.mapDomain_single · cited by 23AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.coeff_mapDomainAddEquiv · cited by 3AddMonoidAlgebra.coeff_ma…AddMonoidAlgebra.mapDomain_sum · cited by 1AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomain_zero · cited by 0AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomainNonUnitalRingHom_comp · cited by 0AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomainNonUnitalRingHom_id · cited by 0AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomain_add · cited by 0AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomain_mul · cited by 0AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomain_vadd · cited by 0AddMonoidAlgebra.mapDomai…Semiring · cited by 13802SemiringFinsupp · cited by 5255FinsuppAddMonoidAlgebra · cited by 649AddMonoidAlgebraAddMonoidAlgebra.coeff · cited by 365AddMonoidAlgebra.coeffFinsupp.mapDomain · cited by 168Finsupp.mapDomainAddMonoidAlgebra.mapDomain · cited by 17AddMonoidAlgebra.mapDomainAddMonoidAlgebra.coeff_mapDom…CITED BYCITES

Cites6

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Cited by9

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