Theorems · Theorem · commutative algebra
MvPowerSeries.coeff_C
∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : DecidableEq σ] (n : σ →₀ ℕ) (a : R),
(MvPowerSeries.coeff n) (MvPowerSeries.C a) = if n = 0 then a else 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 94 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.
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
- Finsuppstatement and proof · cited by 5,255
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPowerSeries.Cstatement · cited by 62
- MvPowerSeries.coeff_monomialproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_C_of_ne_zeroproof · cited by 2
- MvPowerSeries.rescale_zeroproof · cited by 1
- MvPowerSeries.finSuccEquiv_Cproof · cited by 1
- MvPowerSeries.WithPiTopology.continuous_Cproof · cited by 1
- MvPowerSeries.C_surjectiveproof · cited by 0
- MvPowerSeries.LinearTopology.basis_le_iffproof · cited by 0