Theorems · Theorem · commutative algebra
HahnSeries.embDomain_smul
∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Semiring R] [inst_2 : PartialOrder Γ']
(f : Γ ↪o Γ') (r : R) (x : HahnSeries Γ R), HahnSeries.embDomain f (r • x) = r • HahnSeries.embDomain f x- Defined in
- Mathlib.RingTheory.HahnSeries.Addition
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Set.rangeproof · cited by 4,705
- MulZeroClass.mul_zeroproof · cited by 2,091
- OrderEmbeddingstatement and proof · cited by 619
- HahnSeriesstatement and proof · cited by 528
- HahnSeries.coeffproof · cited by 235
- HahnSeries.extproof · cited by 53
- HahnSeries.embDomainstatement · cited by 21
- HahnSeries.embDomain_coeffproof · cited by 10
- HahnSeries.embDomain_of_notMem_rangeproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.embDomainLinearMapproof · cited by 1