Theorems · Theorem · commutative algebra
HahnSeries.orderTop_mul_of_nonzero
Deprecated since 2026-01-02Use HahnSeries.orderTop_mul_of_ne_zero instead.
∀ {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},
x.leadingCoeff * y.leadingCoeff ≠ 0 → (x * y).orderTop = x.orderTop + y.orderTopAlias of HahnSeries.orderTop_mul_of_ne_zero.
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- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement · cited by 12,281
- LinearOrderstatement · cited by 8,572
- WithTopstatement · cited by 3,754
- NonUnitalNonAssocSemiringstatement · cited by 1,081
- HahnSeriesstatement · cited by 528
- IsOrderedCancelAddMonoidstatement · cited by 359
- HahnSeries.orderTopstatement · cited by 103
- HahnSeries.leadingCoeffstatement · cited by 49
- HahnSeries.orderTop_mul_of_ne_zeroproof · cited by 2
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