Theorems · Theorem · commutative algebra
MvPowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero
∀ {σ : Type u_1} {R : Type u_4} [inst : TopologicalSpace R] [inst_1 : Ring R] [IsTopologicalRing R] [T2Space R]
{f : MvPowerSeries σ R}, MvPowerSeries.constantCoeff f = 0 → (∑' (i : ℕ), f ^ i) * (1 - f) = 1Formula for geometric series.
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- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- SummationFilter.unconditionalstatement · cited by 2,068
- T2Spacestatement and proof · cited by 1,351
- tsumstatement · cited by 1,148
- MvPowerSeriesstatement and proof · cited by 659
- IsTopologicalRingstatement and proof · cited by 402
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zeroproof · cited by 3
- Summable.tsum_pow_mul_one_subproof · cited by 3
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