Theorems · Theorem · commutative algebra
HahnSeries.SummableFamily.powers_of_not_orderTop_pos
∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : CommRing R] {x : HahnSeries Γ R},
¬0 < x.orderTop → HahnSeries.SummableFamily.powers x = HahnSeries.SummableFamily.single 0 1- Defined in
- Mathlib.RingTheory.HahnSeries.Summable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement · cited by 3,754
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- HahnSeriesstatement and proof · cited by 528
- zero_powproof · cited by 361
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.coeffproof · cited by 235
- Pi.single_eq_sameproof · cited by 144
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