Theorems · Theorem · commutative algebra
MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero
∀ {σ : Type u_1} {R : Type u_2} [inst : TopologicalSpace R] [inst_1 : Semiring R] {f : MvPowerSeries σ R},
MvPowerSeries.constantCoeff f = 0 → Summable fun x => f ^ xThe geometric series converges if the constant term is zero.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 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.
Cites17
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- SummationFilter.unconditionalstatement · cited by 2,068
- Summablestatement · cited by 778
- LT.lt.trans_leproof · cited by 678
- MvPowerSeriesstatement and proof · cited by 659
- lt_of_lt_of_leproof · cited by 438
- nsmul_eq_mulproof · cited by 369
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- MvPowerSeries.orderproof · cited by 45
Cited by3
Results whose statement or proof uses this declaration.
- PowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zeroproof · cited by 3