Theorems · Theorem · commutative algebra
PowerSeries.Unit_of_divided_by_X_pow_order_nonzero
∀ {k : Type u_2} [inst : Field k] {f : PowerSeries k}, f ≠ 0 → ↑f.Unit_of_divided_by_X_pow_order = f.divXPowOrder- Defined in
- Mathlib.RingTheory.PowerSeries.Inverse
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Unitsproof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.divXPowOrderstatement and proof · cited by 17
- PowerSeries.Inv_divided_by_X_pow_orderproof · cited by 6
- PowerSeries.Unit_of_divided_by_X_pow_orderstatement · cited by 4
- PowerSeries.Inv_divided_by_X_pow_order_leftInvproof · cited by 3
- PowerSeries.Inv_divided_by_X_pow_order_rightInvproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.normUnit_Xproof · cited by 2
- PowerSeries.hasUnitMulPowIrreducibleFactorizationproof · cited by 0