Theorems · Theorem · commutative algebra
MvPowerSeries.constantCoeff_truncTotal_eq_ite
∀ {σ : Type u_1} {R : Type u_2} {n : ℕ} [inst : Finite σ] [inst_1 : CommSemiring R] (p : MvPowerSeries σ R),
MvPolynomial.constantCoeff ((MvPowerSeries.truncTotal n) p) = if 0 < n then MvPowerSeries.constantCoeff p else 0- Defined in
- Mathlib.RingTheory.MvPowerSeries.Trunc
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FiniteCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- Finitestatement and proof · cited by 3,029
- MvPolynomialstatement · cited by 2,140
- map_zeroproof · cited by 1,614
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffproof · cited by 273
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.HasSubst.truncTotalproof · cited by 3
- MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subst_truncTotal_of_leproof · cited by 2