no goals
f : CauSeq ℂ ↑abs
x✝ : ℕ
⊢ (↑(CauSeq.const (↑abs) (limAux f)) x✝).re =
    (↑(CauSeq.const (↑abs) (↑(CauSeq.lim (cauSeqRe f)) + ↑(CauSeq.lim (cauSeqIm f)) * I)) x✝).re
simp [limAux, cauSeqRe, ofReal']
no goals
f : CauSeq ℂ ↑abs
x✝ : ℕ
⊢ (↑(CauSeq.const (↑abs) (limAux f)) x✝).im =
    (↑(CauSeq.const (↑abs) (↑(CauSeq.lim (cauSeqRe f)) + ↑(CauSeq.lim (cauSeqIm f)) * I)) x✝).im
simp [limAux, cauSeqIm, ofReal']