Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_monomial
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : DecidableEq σ] (m n : σ →₀ ℕ) (a : R),
(MvPowerSeries.coeff m) ((MvPowerSeries.monomial n) a) = if m = n then a else 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- Pi.single_applyproof · cited by 78
- LinearMap.projproof · cited by 71
- MvPowerSeries.monomialstatement · cited by 69
- LinearMap.singleproof · cited by 62
- MvPowerSeries.monomial_defproof · cited by 3
Cited by17
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_Xproof · cited by 10
- PowerSeries.coeff_monomialproof · cited by 8
- MvPowerSeries.coeff_expand_smulproof · cited by 7
- MvPowerSeries.coeff_Cproof · cited by 6
- MvPowerSeries.coeff_expand_of_not_dvdproof · cited by 5
- MvPowerSeries.monomial_mul_monomialproof · cited by 5
- MvPolynomial.coe_monomialproof · cited by 5
- MvPowerSeries.coeff_oneproof · cited by 5
- MvPowerSeries.isRestricted_monomialproof · cited by 4
- MvPowerSeries.rescale_eq_substproof · cited by 3
- MvPowerSeries.map_monomialproof · cited by 2
- MvPowerSeries.weightedOrder_monomialproof · cited by 2