Theorems · Definition · commutative algebra
HahnSeries.leadingCoeff
{Γ : Type u_1} → {R : Type u_3} → [inst : PartialOrder Γ] → [inst_1 : Zero R] → HahnSeries Γ R → RA leading coefficient of a Hahn series is the coefficient of a lowest-order nonzero term, or zero if the series vanishes.
- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffproof · cited by 235
- WithTop.recTopCoeproof · cited by 107
- HahnSeries.orderTopproof · cited by 103
Cited by50
Results whose statement or proof uses this declaration.
- HahnSeries.leadingCoeff_zerostatement · cited by 12
- HahnSeries.leadingCoeff_of_ne_zerostatement · cited by 11
- HahnSeries.coeff_mul_order_add_orderstatement · cited by 5
- HahnSeries.leadingCoeff_ne_zerostatement · cited by 4
- HahnSeries.inv_singleproof · cited by 3
- HahnSeries.leadingCoeff_add_eq_leftstatement and proof · cited by 3
- HahnSeries.leadingCoeff_eqstatement and proof · cited by 3
- HahnSeries.leadingCoeff_eq_zerostatement · cited by 3
- HahnSeries.order_mul_of_ne_zerostatement and proof · cited by 3
- HahnSeries.SummableFamily.orderTop_hsum_binomialFamily_posproof · cited by 3
- HahnSeries.leadingCoeff_mul_of_ne_zerostatement and proof · cited by 2
- HahnSeries.leadingCoeff_of_singlestatement · cited by 2