Theorems · Theorem · commutative algebra
HahnSeries.order_single_mul_of_isRegular
∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : NonUnitalNonAssocSemiring R] {g : Γ} {r : R},
IsRegular r → ∀ {x : HahnSeries Γ R}, x ≠ 0 → ((HahnSeries.single g) r * x).order = g + x.order- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- LinearOrderstatement and proof · cited by 8,572
- Nontrivialproof · cited by 2,416
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- subsingleton_or_nontrivialproof · cited by 161
- ZeroHomstatement · cited by 161
- IsRegularstatement and proof · cited by 116
- HahnSeries.singlestatement and proof · cited by 82
- HahnSeries.orderstatement and proof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.unit_auxproof · cited by 2