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Theorems · Theorem · ring theory

AddMonoidAlgebra.mapDomain_single

∀ {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] {f : M → N} {a : M} {r : R},
  AddMonoidAlgebra.mapDomain f (AddMonoidAlgebra.single a r) = AddMonoidAlgebra.single (f a) r
Defined in
Mathlib.Algebra.MonoidAlgebra.MapDomain
Cited by
23 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring

Around this declaration

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

MvPolynomial.rename_X · cited by 48MvPolynomial.rename_XAddMonoidAlgebra.mapDomainRingEquiv_single · cited by 6AddMonoidAlgebra.mapDomai…MvPolynomial.rename_C · cited by 6MvPolynomial.rename_CMvPolynomial.rename_monomial · cited by 5MvPolynomial.rename_monom…Polynomial.toLaurent_C_mul_T · cited by 4Polynomial.toLaurent_C_mu…MvPolynomial.tensorEquivSum_X_tmul_one · cited by 3MvPolynomial.tensorEquivS…MvPolynomial.tensorEquivSum_one_tmul_X · cited by 3MvPolynomial.tensorEquivS…AddMonoidAlgebra.mapDomainAddEquiv_single · cited by 3AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomainBialgHom_single · cited by 3AddMonoidAlgebra.mapDomai…MvPolynomial.tensorEquivSum_X_tmul_X · cited by 2MvPolynomial.tensorEquivS…MvPolynomial.tensorEquivSum_C_tmul_one · cited by 1MvPolynomial.tensorEquivS…AddMonoidAlgebra.mapDomainAlgHom_comp · cited by 1AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomainAlgHom_id · cited by 1AddMonoidAlgebra.mapDomai…MvPolynomial.tensorEquivSum_C_tmul_C · cited by 0MvPolynomial.tensorEquivS…MvPolynomial.tensorEquivSum_one_tmul_C · cited by 0MvPolynomial.tensorEquivS…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringFinsupp.single · cited by 943Finsupp.singleAddMonoidAlgebra · cited by 649AddMonoidAlgebraFinsupp.ext · cited by 399Finsupp.extAddMonoidAlgebra.single · cited by 250AddMonoidAlgebra.singleAddMonoidAlgebra.ext · cited by 90AddMonoidAlgebra.extFinsupp.mapDomain_single · cited by 48Finsupp.mapDomain_singleAddMonoidAlgebra.mapDomain · cited by 17AddMonoidAlgebra.mapDomainAddMonoidAlgebra.coeff_mapDomain · cited by 9AddMonoidAlgebra.coeff_ma…AddMonoidAlgebra.mapDomain_si…CITED BYCITES

Cites10

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Cited by23

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