Theorems · Theorem · commutative algebra
HahnSeries.support_nonempty_iff
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {x : HahnSeries Γ R},
x.support.Nonempty ↔ x ≠ 0- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 94 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.Nonemptystatement and proof · cited by 2,627
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffproof · cited by 235
- HahnSeries.supportstatement · cited by 84
- Function.support_nonempty_iffproof · cited by 4
- HahnSeries.coeff_fun_eq_zero_iffproof · cited by 2
Cited by28
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_of_ne_zerostatement · cited by 17
- HahnSeries.order_of_nestatement · cited by 13
- HahnSeries.coeff_eq_zero_of_lt_orderTopproof · cited by 9
- HahnSeries.orderTop_singleproof · cited by 6
- HahnSeries.order_le_of_coeff_ne_zeroproof · cited by 6
- HahnSeries.coeff_orderTop_neproof · cited by 5
- HahnSeries.order_singleproof · cited by 4
- 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.order_mul_of_ne_zeroproof · cited by 3
- HahnSeries.coeff_eq_zero_of_lt_orderproof · cited by 3