let c, d be Real; ( 0 < c implies lim (rseq (0,1,c,d)) = 0 )
set f = rseq (0,1,c,d);
assume A1:
0 < c
; lim (rseq (0,1,c,d)) = 0
then A2:
rseq (0,1,c,d) is convergent
by Lm5;
for p being Real st 0 < p holds
ex n being Nat st
for m being Nat st n <= m holds
|.(((rseq (0,1,c,d)) . m) - 0).| < p
by A1, Lm4;
hence
lim (rseq (0,1,c,d)) = 0
by A2, SEQ_2:def 7; verum