Theorems · Theorem · commutative algebra
HahnSeries.single_ne_zero
∀ {Γ : Type u_1} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] {a : Γ} {r : R},
r ≠ 0 → (HahnSeries.single a) r ≠ 0- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 3 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- HahnSeriesstatement · cited by 528
- ZeroHomstatement · cited by 161
- HahnSeries.singlestatement and proof · cited by 82
- HahnSeries.single_eq_zeroproof · cited by 2
- HahnSeries.single_injectiveproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_singleproof · cited by 6
- HahnSeries.order_singleproof · cited by 4
- HahnSeries.order_lt_order_of_eq_add_singleproof · cited by 1