Theorems · Theorem · commutative algebra
HahnSeries.support_embDomain_subset
∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] [inst_2 : PartialOrder Γ']
{f : Γ ↪o Γ'} {x : HahnSeries Γ R}, (HahnSeries.embDomain f x).support ⊆ ⇑f '' x.support- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderZeroPartialOrder
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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.imagestatement and proof · cited by 5,609
- OrderEmbeddingstatement and proof · cited by 619
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.supportstatement and proof · cited by 84
- HahnSeries.embDomainstatement and proof · cited by 21
- HahnSeries.mem_supportproof · cited by 10
- HahnSeries.embDomain_notin_image_supportproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- HahnSeries.orderTop_embDomainproof · cited by 1
- HahnSeries.embDomain_mulproof · cited by 0