Theorems · Theorem · commutative algebra
PowerSeries.coeff_C_mul
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (φ : PowerSeries R) (a : R),
(PowerSeries.coeff n) (PowerSeries.C a * φ) = a * (PowerSeries.coeff n) φ- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 95 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 · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsupp.singleproof · cited by 943
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement · cited by 324
- PowerSeries.Cstatement · cited by 76
- MvPowerSeries.coeff_C_mulproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- PowerSeries.monomial_eq_C_mul_X_powproof · cited by 4
- PowerSeries.subst_substInv_rightproof · cited by 2
- PowerSeries.smul_eq_C_mulproof · cited by 2
- PowerSeries.rescale_Xproof · cited by 1
- PowerSeries.eq_of_le_of_X_notMem_of_fg_of_isPrimeproof · cited by 1
- PowerSeries.coeff_subst_sum_C_substInvFun_mul_X_pow_sub_Xproof · cited by 1
- PowerSeries.coeff_C_mul_X_powproof · cited by 0
- PowerSeries.trunc_C_mulproof · cited by 0