Theorems · Theorem · commutative algebra
MvPowerSeries.monomial_mul_monomial
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (m n : σ →₀ ℕ) (a b : R),
(MvPowerSeries.monomial m) a * (MvPowerSeries.monomial n) b = (MvPowerSeries.monomial (m + n)) (a * b)- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MulZeroClass.zero_mulproof · cited by 1,625
- le_rflproof · cited by 1,558
- MvPowerSeriesstatement · cited by 659
- add_tsub_cancel_rightproof · cited by 172
- tsub_add_cancel_of_leproof · cited by 112
- MvPowerSeries.monomialstatement and proof · cited by 69
- MvPowerSeries.extproof · cited by 58
Cited by5
Results whose statement or proof uses this declaration.
- MvPowerSeries.X_pow_eqproof · cited by 3
- MvPowerSeries.prod_monomialproof · cited by 2
- MvPowerSeries.monomial_mem_nonzeroDivisorsLeftproof · cited by 1
- MvPowerSeries.monomial_mem_nonzeroDivisorsRightproof · cited by 1
- PowerSeries.monomial_mul_monomialproof · cited by 0