Theorems · Theorem · commutative algebra
HahnSeries.orderTop_mul
∀ {Γ : Type u_1} {R : Type u_3} [inst : AddCommMonoid Γ] [inst_1 : LinearOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
[inst_3 : NonUnitalNonAssocSemiring R] (x y : HahnSeries Γ R) [NoZeroDivisors R],
(x * y).orderTop = x.orderTop + y.orderTop- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement · cited by 3,754
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NoZeroDivisorsstatement and proof · cited by 545
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.orderTopstatement and proof · cited by 103
- HahnSeries.orderTop_zeroproof · cited by 22
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