Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_add_monomial_mul
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (m n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R),
(MvPowerSeries.coeff (m + n)) ((MvPowerSeries.monomial m) a * φ) = a * (MvPowerSeries.coeff n) φ- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 4 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.
Cites12
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
- le_rflproof · cited by 1,558
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement and proof · cited by 273
- MvPowerSeries.monomialstatement · cited by 69
- add_tsub_cancel_leftproof · cited by 42
- le_add_rightproof · cited by 21
- MvPowerSeries.coeff_monomial_mulproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_succ_X_mulproof · cited by 4
- MvPowerSeries.coeff_C_mulproof · cited by 4
- MvPowerSeries.commute_monomialproof · cited by 1
- MvPowerSeries.one_mulproof · cited by 0