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Theorems · Theorem · ring theory

MonoidAlgebra.coeff_mapDomain

∀ {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] (f : M → N) (x : MonoidAlgebra R M),
  (MonoidAlgebra.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.

MonoidAlgebra.mapDomain_single · cited by 12MonoidAlgebra.mapDomain_s…MonoidAlgebra.coeff_mapDomainAddEquiv · cited by 3MonoidAlgebra.coeff_mapDo…MonoidAlgebra.mapDomain_sum · cited by 1MonoidAlgebra.mapDomain_s…MonoidAlgebra.mapDomain_add · cited by 0MonoidAlgebra.mapDomain_a…MonoidAlgebra.mapDomain_mul · cited by 0MonoidAlgebra.mapDomain_m…MonoidAlgebra.mapDomain_smul · cited by 0MonoidAlgebra.mapDomain_s…MonoidAlgebra.mapDomain_zero · cited by 0MonoidAlgebra.mapDomain_z…MonoidAlgebra.mapDomainNonUnitalRingHom_comp · cited by 0MonoidAlgebra.mapDomainNo…MonoidAlgebra.mapDomainNonUnitalRingHom_id · cited by 0MonoidAlgebra.mapDomainNo…Semiring · cited by 13802SemiringFinsupp · cited by 5255FinsuppMonoidAlgebra · cited by 590MonoidAlgebraMonoidAlgebra.coeff · cited by 224MonoidAlgebra.coeffFinsupp.mapDomain · cited by 168Finsupp.mapDomainMonoidAlgebra.mapDomain · cited by 15MonoidAlgebra.mapDomainMonoidAlgebra.coeff_mapDomainCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.