Theorems · Theorem · commutative algebra
Polynomial.IsDistinguishedAt.algEquivQuotient.congr_simp
∀ {A : Type u_1} [inst : CommRing A] {g : Polynomial A} {I I_1 : Ideal A} (e_I : I = I_1) (H : g.IsDistinguishedAt I)
[inst_1 : IsAdicComplete I A], H.algEquivQuotient = ⋯.algEquivQuotient- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsAdicComplete
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- AlgEquivstatement · cited by 1,681
- Ideal.spanstatement · cited by 948
- PowerSeriesstatement · cited by 797
- IsAdicCompletestatement and proof · cited by 124
- Polynomial.toPowerSeriesstatement · cited by 96
- Polynomial.IsDistinguishedAtstatement and proof · cited by 15
- Polynomial.IsDistinguishedAt.algEquivQuotientstatement and proof · cited by 4
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