Theorems · Theorem · commutative algebra
PowerSeries.coeff_C
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (a : R), (PowerSeries.coeff n) (PowerSeries.C a) = if n = 0 then a else 0- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 97 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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement and proof · cited by 324
- PowerSeries.Cstatement · cited by 76
- PowerSeries.coeff_monomialproof · cited by 8
- PowerSeries.monomial_zero_eq_C_applyproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_oneproof · cited by 17
- PowerSeries.coeff_zero_Cproof · cited by 4
- HahnSeries.ofPowerSeries_Cproof · cited by 3
- PowerSeries.coeff_C_of_ne_zeroproof · cited by 3
- PowerSeries.rescale_zeroproof · cited by 3
- PowerSeries.eq_X_mul_shift_add_constproof · cited by 2
- PowerSeries.eq_shift_mul_X_add_constproof · cited by 2
- PowerSeries.map_Cproof · cited by 2
- MvPowerSeries.finSuccEquiv_Cproof · cited by 1
- MvPowerSeries.finSuccEquiv_X_succproof · cited by 0
- PowerSeries.trunc_Cproof · cited by 0