theorem :: CSSPACE2:16

for c being Complex
for seq1 being Real_Sequence
for seq being Complex_Sequence st seq is convergent & seq1 is convergent holds
for rseq being Real_Sequence st ( for i being Nat holds rseq . i = (|.((seq . i) - c).| * |.((seq . i) - c).|) + (seq1 . i) ) holds
( rseq is convergent & lim rseq = (|.((lim seq) - c).| * |.((lim seq) - c).|) + (lim seq1) ) by Lm23;