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Theorems · Theorem · commutative algebra

MvPowerSeries.coeff_monomial

∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : DecidableEq σ] (m n : σ →₀ ℕ) (a : R),
  (MvPowerSeries.coeff m) ((MvPowerSeries.monomial n) a) = if m = n then a else 0
Defined in
Mathlib.RingTheory.MvPowerSeries.Basic
Cited by
17 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringDecidableEq

Around this declaration

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

MvPowerSeries.coeff_X · cited by 10MvPowerSeries.coeff_XPowerSeries.coeff_monomial · cited by 8PowerSeries.coeff_monomialMvPowerSeries.coeff_expand_smul · cited by 7MvPowerSeries.coeff_expan…MvPowerSeries.coeff_C · cited by 6MvPowerSeries.coeff_CMvPowerSeries.coeff_expand_of_not_dvd · cited by 5MvPowerSeries.coeff_expan…MvPowerSeries.monomial_mul_monomial · cited by 5MvPowerSeries.monomial_mu…MvPolynomial.coe_monomial · cited by 5MvPolynomial.coe_monomialMvPowerSeries.coeff_one · cited by 5MvPowerSeries.coeff_oneMvPowerSeries.isRestricted_monomial · cited by 4MvPowerSeries.isRestricte…MvPowerSeries.rescale_eq_subst · cited by 3MvPowerSeries.rescale_eq_…MvPowerSeries.map_monomial · cited by 2MvPowerSeries.map_monomialMvPowerSeries.weightedOrder_monomial · cited by 2MvPowerSeries.weightedOrd…PowerSeries.HasSubst.monomial · cited by 1HasSubst.monomialMvPowerSeries.coeff_X_pow · cited by 1MvPowerSeries.coeff_X_powPowerSeries.toMvPowerSeries_coeff_eq_zero · cited by 1PowerSeries.toMvPowerSeri…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapFinsupp · cited by 5255FinsuppMvPowerSeries · cited by 659MvPowerSeriesMvPowerSeries.coeff · cited by 273MvPowerSeries.coeffPi.single_apply · cited by 78Pi.single_applyLinearMap.proj · cited by 71LinearMap.projMvPowerSeries.monomial · cited by 69MvPowerSeries.monomialLinearMap.single · cited by 62LinearMap.singleMvPowerSeries.monomial_def · cited by 3MvPowerSeries.monomial_defLinearMap.proj_apply · cited by 1LinearMap.proj_applyLinearMap.single_apply · cited by 1LinearMap.single_applyMvPowerSeries.coeff_monomialCITED BYCITES

Cites14

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

Cited by17

Results whose statement or proof uses this declaration.