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Theorems · Theorem · complex analysis

RCLike.hasSum_im

∀ {α : Type u_1} (𝕜 : Type u_2) [inst : RCLike 𝕜] {L : SummationFilter α} {f : α → 𝕜} {x : 𝕜},
  HasSum f x L → HasSum (fun x => RCLike.im (f x)) (RCLike.im x) L
Defined in
Mathlib.Analysis.Complex.Basic
Cited by
2 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLike
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RCLike.hasSum_iff · cited by 1RCLike.hasSum_iffComplex.hasSum_im · cited by 0Complex.hasSum_imDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealAddMonoidHom · cited by 3230AddMonoidHomRCLike · cited by 2829RCLikeSummationFilter · cited by 607SummationFilterHasSum · cited by 518HasSumAddMonoid.toZero · cited by 325AddMonoid.toZeroRCLike.im · cited by 161RCLike.imContinuousLinearMap.hasSum · cited by 13ContinuousLinearMap.hasSumRCLike.imCLM · cited by 8RCLike.imCLMRCLike.hasSum_imCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.