Theorems · Definition · commutative algebra
PowerSeries.firstUnitCoeff
{k : Type u_2} → [inst : Field k] → {f : PowerSeries k} → f ≠ 0 → kˣfirstUnitCoeff is the non-zero coefficient whose index is f.order, seen as a unit of the
field. It is obtained using divided_by_X_pow_order, defined in PowerSeries.Order.
- Defined in
- Mathlib.RingTheory.PowerSeries.Inverse
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 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.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Unitsstatement · cited by 2,804
- PowerSeriesstatement and proof · cited by 797
- Invertibleproof · cited by 549
- PowerSeries.constantCoeffproof · cited by 126
- PowerSeries.divXPowOrderproof · cited by 17
- invertibleOfNonzeroproof · cited by 12
- unitOfInvertibleproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.Inv_divided_by_X_pow_orderproof · cited by 6
- PowerSeries.Inv_divided_by_X_pow_order_leftInvproof · cited by 3
- PowerSeries.Inv_divided_by_X_pow_order_rightInvproof · cited by 3