Theorems · Theorem · commutative algebra
HahnSeries.coeff_mul_order_add_order
∀ {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 * y).coeff (x.order + y.order) = x.leadingCoeff * y.leadingCoeff- Cited by
- 5 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.coeffstatement · cited by 235
- HahnSeries.orderstatement · cited by 52
- HahnSeries.leadingCoeffstatement · cited by 49
- HahnModule.coeff_smul_order_add_orderproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- HahnSeries.order_mul_of_ne_zeroproof · cited by 3
- HahnSeries.orderTop_mul_of_ne_zeroproof · cited by 2
- HahnSeries.leadingCoeff_mul_of_ne_zeroproof · cited by 2
- HahnSeries.order_mulproof · cited by 1
- HahnSeries.isUnit_iffproof · cited by 0