Theorems · Theorem · commutative algebra
HahnSeries.orderTop_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.orderTop = ↑(⋯.min ⋯)- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 17 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.
Cites10
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
- WithTopstatement · cited by 3,754
- Set.Nonemptystatement · cited by 2,627
- WithTop.somestatement · cited by 1,128
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.orderTopstatement · cited by 103
- HahnSeries.supportstatement · cited by 84
- Set.IsWF.minstatement · cited by 47
- HahnSeries.isWF_supportstatement · cited by 33
- HahnSeries.support_nonempty_iffstatement · cited by 28
Cited by17
Results whose statement or proof uses this declaration.
- HahnSeries.coeff_eq_zero_of_lt_orderTopproof · cited by 9
- HahnSeries.orderTop_singleproof · cited by 6
- HahnSeries.coeff_orderTop_neproof · cited by 5
- HahnSeries.orderTop_add_eq_leftproof · cited by 4
- HahnSeries.orderTop_le_of_coeff_ne_zeroproof · cited by 4
- HahnSeries.order_eq_orderTop_of_ne_zeroproof · cited by 4
- HahnSeries.leadingCoeff_eqproof · cited by 3
- HahnSeries.orderTop_eq_of_leproof · cited by 3
- HahnSeries.untop_orderTop_of_ne_zeroproof · cited by 2
- HahnSeries.zero_lt_orderTop_iffproof · cited by 2
- HahnSeries.coeff_untop_eq_leadingCoeffproof · cited by 2
- HahnSeries.orderTop_smul_not_ltproof · cited by 2