Theorems · Theorem · commutative algebra
HahnModule.single_zero_smul_eq_smul
∀ {Γ' : Type u_2} {R : Type u_3} {V : Type u_5} [inst : PartialOrder Γ'] [inst_1 : AddCommMonoid V] (Γ : Type u_6)
[inst_2 : AddCommMonoid Γ] [inst_3 : PartialOrder Γ] [inst_4 : AddAction Γ Γ'] [inst_5 : IsOrderedCancelVAdd Γ Γ']
[inst_6 : MulZeroClass R] [inst_7 : SMulWithZero R V] {r : R} {x : HahnModule Γ' R V},
(HahnSeries.single 0) r • x = r • x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- AddActionstatement and proof · cited by 820
- HahnSeriesstatement · cited by 528
- MulZeroClassstatement and proof · cited by 232
- ZeroHomstatement · cited by 161
- SMulWithZerostatement and proof · cited by 113
- HahnSeries.singlestatement and proof · cited by 82
- HahnModulestatement and proof · cited by 51
- IsOrderedCancelVAddstatement and proof · cited by 31
- HahnModule.extproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.powerSeriesFamily_smulproof · cited by 0