Theorems · Theorem · commutative algebra
HahnSeries.coeff_eq_zero_of_lt_orderTop
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {x : HahnSeries Γ R} {i : Γ},
↑i < x.orderTop → x.coeff i = 0- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 98 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.
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- eq_or_neproof · cited by 1,117
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffstatement and proof · cited by 235
- HahnSeries.orderTopstatement and proof · cited by 103
- WithTop.coe_lt_coeproof · cited by 47
- HahnSeries.isWF_supportproof · cited by 33
- HahnSeries.support_nonempty_iffproof · cited by 28
- HahnSeries.orderTop_of_ne_zeroproof · cited by 17
- HahnSeries.mem_supportproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_add_eq_leftproof · cited by 4
- HahnSeries.SummableFamily.orderTop_hsum_binomialFamily_posproof · cited by 3
- HahnSeries.leadingCoeff_add_eq_leftproof · cited by 3
- HahnSeries.leadingCoeff_pos_iffproof · cited by 2
- HahnSeries.abs_lt_abs_of_orderTop_ofLexproof · cited by 1
- HahnEmbedding.Partial.coeff_eq_zero_of_memproof · cited by 1
- HahnSeries.le_orderTop_iff_forallproof · cited by 1
- PowerSeries.coeff_heval_zeroproof · cited by 0