Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_monomial_same
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (n : σ →₀ ℕ) (a : R),
(MvPowerSeries.coeff n) ((MvPowerSeries.monomial n) a) = a- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 67 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.
Cites10
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 and proof · cited by 273
- Pi.single_eq_sameproof · cited by 144
- MvPowerSeries.monomialstatement · cited by 69
- MvPowerSeries.monomial_defproof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_mul_monomialproof · cited by 5
- MvPowerSeries.coeff_monomial_mulproof · cited by 3
- MvPowerSeries.WithPiTopology.hasSum_of_monomials_selfproof · cited by 3
- MvPowerSeries.rescale_eq_substproof · cited by 3
- MvPowerSeries.weightedOrder_monomialproof · cited by 2
- MvPowerSeries.rename_eq_substproof · cited by 2
- PowerSeries.coeff_monomial_sameproof · cited by 2
- MvPowerSeries.map_algebraMap_eq_subst_Xproof · cited by 1
- MvPowerSeries.coeff_zero_Cproof · cited by 1
- MvPowerSeries.coeff_index_single_self_Xproof · cited by 1
- MvPowerSeries.LinearTopology.basis_le_iffproof · cited by 0
- MvPowerSeries.coeff_comp_monomialproof · cited by 0