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Theorems · Theorem · commutative algebra

MvPowerSeries.coeff_truncTotal

∀ {σ : Type u_1} {R : Type u_2} {n : ℕ} [inst : Finite σ] [inst_1 : CommSemiring R] (p : MvPowerSeries σ R)
  {x : σ →₀ ℕ}, Finsupp.degree x < n → MvPolynomial.coeff x ((MvPowerSeries.truncTotal n) p) = (MvPowerSeries.coeff x) p
Defined in
Mathlib.RingTheory.MvPowerSeries.Trunc
Cited by
10 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FiniteCommSemiring

Around this declaration

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

MvPowerSeries.coeff_truncTotal_eq_ite · cited by 3MvPowerSeries.coeff_trunc…MvPowerSeries.coeff_truncTotal_pow · cited by 2MvPowerSeries.coeff_trunc…MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sum · cited by 2MvPowerSeries.truncTotal_…MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_truncTotal_of_le · cited by 1MvPowerSeries.truncTotal_…MvPowerSeries.truncTotal_mul_sub_mul_truncTotal_mem_pow_idealOfVars · cited by 0MvPowerSeries.truncTotal_…MvPowerSeries.toAdicCompletion_coe · cited by 0MvPowerSeries.toAdicCompl…MvPowerSeries.truncTotal_pow_eq_truncTotal_truncTotal_pow · cited by 0MvPowerSeries.truncTotal_…MvPowerSeries.truncTotal_sub_truncTotal_mem_pow_idealOfVars · cited by 0MvPowerSeries.truncTotal_…MvPowerSeries.mk_truncTotal_toAdicCompletionInv · cited by 0MvPowerSeries.mk_truncTot…MvPowerSeries.coeff_toAdicCompletion_val_apply_out · cited by 0MvPowerSeries.coeff_toAdi…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapFinsupp · cited by 5255FinsuppAddMonoidHom · cited by 3230AddMonoidHomFinite · cited by 3029FiniteMvPolynomial · cited by 2140MvPolynomialMvPowerSeries · cited by 659MvPowerSeriesMvPolynomial.coeff · cited by 315MvPolynomial.coeffMvPowerSeries.coeff · cited by 273MvPowerSeries.coeffFinsupp.degree · cited by 94Finsupp.degreeMvPowerSeries.truncTotal · cited by 28MvPowerSeries.truncTotalFinsupp.finite_of_degree_lt · cited by 5Finsupp.finite_of_degree_…MvPowerSeries.coeff_truncFinset_of_mem · cited by 3MvPowerSeries.coeff_trunc…MvPowerSeries.coeff_truncTotalCITED BYCITES

Cites15

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Cited by10

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