Theorems · Theorem · commutative algebra
HahnSeries.order_mul_of_ne_zero
∀ {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).order = x.order + y.order- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- LinearOrderstatement and proof · cited by 8,572
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.coeffproof · cited by 235
- HahnSeries.orderstatement and proof · cited by 52
- HahnSeries.leadingCoeffstatement and proof · cited by 49
- Set.IsWF.minproof · cited by 47
Cited by3
Results whose statement or proof uses this declaration.
- HahnSeries.leadingCoeff_mul_of_ne_zeroproof · cited by 2
- HahnSeries.order_single_mul_of_isRegularproof · cited by 1
- HahnSeries.order_mul_of_nonzeroproof · cited by 0