Theorems · Theorem · commutative algebra
PowerSeries.IsWeierstrassDivisionAt.degree_lt
∀ {A : Type u_1} [inst : CommRing A] {f g q : PowerSeries A} {r : Polynomial A} {I : Ideal A},
f.IsWeierstrassDivisionAt g q r I → r.degree < ↑((PowerSeries.map (Ideal.Quotient.mk I)) g).order.toNat- Cited by
- 8 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- WithBotstatement · cited by 1,498
- PowerSeriesstatement and proof · cited by 797
- Polynomial.degreestatement · cited by 643
- Ideal.Quotient.mkstatement · cited by 610
- ENat.toNatstatement · cited by 143
- PowerSeries.orderstatement · cited by 92
Cited by8
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivision.elimproof · cited by 3
- PowerSeries.IsWeierstrassDivisionAt.smulproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.mod_smulproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.div_smulproof · cited by 2
- PowerSeries.IsWeierstrassDivisionAt.addproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.div_addproof · cited by 1
- PowerSeries.IsWeierstrassDivision.isWeierstrassFactorizationproof · cited by 1
- PowerSeries.IsWeierstrassDivisorAt.mod_addproof · cited by 1