Theorems · Theorem · commutative algebra
LaurentSeries.coeff_zero_of_lt_valuation
∀ (K : Type u_2) [inst : Field K] {n D : ℤ} {f : LaurentSeries K},
Valued.v f ≤ WithZero.exp (-D) → n < D → f.coeff n = 0The coefficients of a Laurent series vanish in degree strictly less than its valuation.
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 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.
Cites41
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
- Fieldstatement and proof · cited by 7,404
- le_reflproof · cited by 2,061
- add_commproof · cited by 1,535
- le_of_ltproof · cited by 1,175
- map_mulproof · cited by 1,137
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- Multiplicativestatement and proof · cited by 875
- Valuationstatement · cited by 823
- PowerSeriesproof · cited by 797
- WithZerostatement and proof · cited by 586
Cited by2
Results whose statement or proof uses this declaration.
- LaurentSeries.valuation_le_iff_coeff_lt_eq_zeroproof · cited by 3
- LaurentSeries.eq_coeff_of_valuation_sub_ltproof · cited by 2