Theorems · Theorem · commutative algebra
PowerSeries.as_tsum
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : TopologicalSpace R] [T2Space R] (f : PowerSeries R),
f = ∑' (d : ℕ), (PowerSeries.monomial d) ((PowerSeries.coeff d) f)If the coefficient space is T2, then the power series is tsum of its monomials
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- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- SummationFilter.unconditionalstatement · cited by 2,068
- T2Spacestatement and proof · cited by 1,351
- tsumstatement · cited by 1,148
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement · cited by 324
- HasSum.tsum_eqproof · cited by 150
- PowerSeries.monomialstatement · cited by 29
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