Theorems · Theorem · commutative algebra

MvPowerSeries.coeff_toAdicCompletionInv

∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] {x : σ →₀ ℕ}
  {f : AdicCompletion (MvPolynomial.idealOfVars σ R) (MvPolynomial σ R)},
  (MvPowerSeries.coeff x) (MvPowerSeries.toAdicCompletionInv σ R f) =
    MvPolynomial.coeff x (Quotient.out (↑f (Finsupp.degree x + 1)))

Defined in: Mathlib.RingTheory.MvPowerSeries.Equiv
Cited by: 1 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites21

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

DFunLike.coestatement and proof · cited by 62,936
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
LinearMapstatement · cited by 10,215
Top.topstatement · cited by 9,680
Submodulestatement · cited by 7,192
Finsuppstatement and proof · cited by 5,255
Idealstatement · cited by 4,748
AddMonoidHomstatement · cited by 3,230
HasQuotient.Quotientstatement · cited by 2,301
MvPolynomialstatement and proof · cited by 2,140
MvPowerSeriesstatement · cited by 659

Cited by1

Results whose statement or proof uses this declaration.

MvPowerSeries.mk_truncTotal_toAdicCompletionInvproof · cited by 0