Theorems · Theorem · commutative algebra
HahnSeries.single_div_single
∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommGroup Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedAddMonoid Γ]
[inst_3 : Field R] (a b : Γ) (r s : R),
(HahnSeries.single a) r / (HahnSeries.single b) s = (HahnSeries.single (a - b)) (r / s)- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- sub_eq_add_negproof · cited by 1,023
- div_eq_mul_invproof · cited by 715
- HahnSeriesstatement and proof · cited by 528
- ZeroHomstatement · cited by 161
- HahnSeries.singlestatement and proof · cited by 82
- HahnSeries.single_mul_singleproof · cited by 6
- HahnSeries.inv_singleproof · cited by 3
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