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Theorems · Theorem · ring theory

AddMonoidAlgebra.ext

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {x y : AddMonoidAlgebra R M}, x.coeff = y.coeff → x = y

Alias of the forward direction of AddMonoidAlgebra.coeff_inj.

Defined in
Mathlib.Algebra.MonoidAlgebra.Defs
Cited by
90 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MvPolynomial.ext · cited by 61MvPolynomial.extAddMonoidAlgebra.mapDomain_single · cited by 23AddMonoidAlgebra.mapDomai…Polynomial.X_mul · cited by 12Polynomial.X_mulAddMonoidAlgebra.smul_single · cited by 9AddMonoidAlgebra.smul_sin…AddMonoidAlgebra.mapAlgHom_single · cited by 9AddMonoidAlgebra.mapAlgHo…AddMonoidAlgebra.scalarTensorEquiv_tmul · cited by 8AddMonoidAlgebra.scalarTe…MvPolynomial.support_sum_monomial_coeff · cited by 6MvPolynomial.support_sum_…AddMonoidAlgebra.sum_coeff_single · cited by 6AddMonoidAlgebra.sum_coef…LaurentPolynomial.ext · cited by 6LaurentPolynomial.extAddMonoidAlgebra.map_single · cited by 4AddMonoidAlgebra.map_sing…AddMonoidAlgebra.uniqueRingEquiv_symm_apply · cited by 3AddMonoidAlgebra.uniqueRi…AddMonoidAlgebra.divOf_add_modOf · cited by 3AddMonoidAlgebra.divOf_ad…AddMonoidAlgebra.mapDomainBialgHom_comp · cited by 2AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mul_of'_divOf · cited by 2AddMonoidAlgebra.mul_of'_…AddMonoidAlgebra.mul_of'_modOf · cited by 2AddMonoidAlgebra.mul_of'_…Semiring · cited by 13802SemiringFinsupp · cited by 5255FinsuppAddMonoidAlgebra · cited by 649AddMonoidAlgebraAddMonoidAlgebra.coeff · cited by 365AddMonoidAlgebra.coeffAddMonoidAlgebra.coeff_inj · cited by 5AddMonoidAlgebra.coeff_injAddMonoidAlgebra.extCITED BYCITES

Cites5

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

Cited by90

Results whose statement or proof uses this declaration.