Theorems · Theorem · commutative algebra
MvPowerSeries.truncTotal_eq_sum
∀ {σ : Type u_1} {R : Type u_2} {n : ℕ} [inst : Finite σ] [inst_1 : CommSemiring R] (p : MvPowerSeries σ R),
↑((MvPowerSeries.truncTotal n) p) = ∑ i ∈ Finset.range n, (MvPowerSeries.homogeneousComponent i) p- Defined in
- Mathlib.RingTheory.MvPowerSeries.Trunc
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 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.
Cites21
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
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement · cited by 5,195
- Finitestatement and proof · cited by 3,029
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialstatement · cited by 2,140
- Finset.rangestatement and proof · cited by 1,341
- MvPowerSeriesstatement and proof · cited by 659
- map_sumproof · cited by 455
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.truncTotal_subst_of_leproof · cited by 1
- MvPowerSeries.truncTotal_subst_eq_truncTotal_truncTotal_substproof · cited by 0