Theorems · Theorem · commutative algebra
MvPowerSeries.WithPiTopology.hasSum_of_monomials_self
∀ {σ : Type u_1} {R : Type u_2} [inst : TopologicalSpace R] [inst_1 : Semiring R] (f : MvPowerSeries σ R),
HasSum (fun d => (MvPowerSeries.monomial d) ((MvPowerSeries.coeff d) f)) fA multivariate power series is the sum (in the sense of summable families) of its monomials
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MvPowerSeriesstatement and proof · cited by 659
- HasSumstatement and proof · cited by 518
- MvPowerSeries.coeffstatement and proof · cited by 273
- MvPowerSeries.monomialstatement and proof · cited by 69
- MvPowerSeries.coeff_monomial_sameproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.hasSum_eval₂proof · cited by 3
- PowerSeries.hasSum_of_monomials_selfproof · cited by 2
- MvPowerSeries.WithPiTopology.as_tsumproof · cited by 0