Theorems · Theorem · commutative algebra
HahnSeries.leadingCoeff_of_ne_zero
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {x : HahnSeries Γ R} (hx : x ≠ 0),
x.leadingCoeff = x.coeff (x.orderTop.untop ⋯)- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 99 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement · cited by 3,754
- WithTop.someproof · cited by 1,128
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffstatement and proof · cited by 235
- WithTop.recTopCoeproof · cited by 107
- HahnSeries.orderTopstatement and proof · cited by 103
- HahnSeries.leadingCoeffstatement · cited by 49
- Set.IsWF.minproof · cited by 47
- WithTop.untopstatement · cited by 36
- HahnSeries.isWF_supportproof · cited by 33
Cited by11
Results whose statement or proof uses this declaration.
- HahnSeries.leadingCoeff_eq_zeroproof · cited by 3
- HahnSeries.leadingCoeff_eqproof · cited by 3
- HahnSeries.leadingCoeff_add_eq_leftproof · cited by 3
- HahnSeries.leadingCoeff_pos_iffproof · cited by 2
- HahnSeries.coeff_untop_eq_leadingCoeffproof · cited by 2
- HahnSeries.orderTop_sub_neproof · cited by 2
- HahnSeries.leadingCoeff_negproof · cited by 1
- HahnSeries.SummableFamily.hsum_leadingCoeff_of_leproof · cited by 1
- HahnSeries.addOppositeEquiv_leadingCoeffproof · cited by 1
- HahnModule.coeff_smul_order_add_orderproof · cited by 1