Theorems · Theorem · commutative algebra
MvPowerSeries.le_weightedOrder_mul
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f g : MvPowerSeries σ R},
MvPowerSeries.weightedOrder w f + MvPowerSeries.weightedOrder w g ≤ MvPowerSeries.weightedOrder w (f * g)The weightedOrder of the product of two formal power series
is at least the sum of their orders.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsuppproof · cited by 5,255
- ENatstatement and proof · cited by 4,985
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- map_addproof · cited by 964
- add_le_addproof · cited by 666
- MvPowerSeriesstatement and proof · cited by 659
- Nat.cast_addproof · cited by 586
- lt_of_lt_of_leproof · cited by 438
- MvPowerSeries.coeffproof · cited by 273
Cited by7
Results whose statement or proof uses this declaration.
- MvPowerSeries.le_weightedOrder_prodproof · cited by 3
- MvPowerSeries.weightedOrder_mulproof · cited by 2
- MvPowerSeries.le_weightedOrder_powproof · cited by 2
- MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrderproof · cited by 2
- MvPowerSeries.le_order_mulproof · cited by 1
- MvPowerSeries.coeff_mul_right_one_sub_of_lt_weightedOrderproof · cited by 1
- MvPowerSeries.weightedOrder_mul_geproof · cited by 0