Theorems · Definition · commutative algebra
HahnSeries.embDomain
{Γ : Type u_1} →
{Γ' : Type u_2} →
{R : Type u_3} →
[inst : PartialOrder Γ] →
[inst_1 : Zero R] → [inst_2 : PartialOrder Γ'] → Γ ↪o Γ' → HahnSeries Γ R → HahnSeries Γ' RExtends the domain of a HahnSeries by an OrderEmbedding.
- Defined in
- Mathlib.RingTheory.HahnSeries.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 17 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- Set.imageproof · cited by 5,609
- OrderEmbeddingstatement and proof · cited by 619
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffproof · cited by 235
- HahnSeries.supportproof · cited by 84
Cited by24
Results whose statement or proof uses this declaration.
- HahnSeries.embDomain_coeffstatement · cited by 10
- HahnSeries.embDomain_notin_image_supportstatement · cited by 7
- HahnSeries.embDomain_of_notMem_rangestatement · cited by 6
- HahnSeries.ofPowerSeries_Xproof · cited by 5
- HahnSeries.embDomainOrderEmbeddingproof · cited by 4
- HahnSeries.ofPowerSeries_Cproof · cited by 3
- HahnSeries.embDomain_singlestatement and proof · cited by 2
- HahnSeries.ofPowerSeries_applystatement · cited by 2
- HahnSeries.support_embDomain_subsetstatement and proof · cited by 2
- HahnSeries.embDomainRingHomproof · cited by 2
- HahnSeries.embDomain_zerostatement · cited by 1
- HahnSeries.ofPowerSeries_apply_coeffproof · cited by 1