reserve Rseq, Rseq1, Rseq2 for Function of [:NAT,NAT:],REAL;
reserve rseq1,rseq2 for convergent Real_Sequence;
reserve n,m,N,M for Nat;
reserve e,r for Real;
reserve Pseq for P-convergent Function of [:NAT,NAT:],REAL;

theorem
for Psubseq be subsequence of Pseq holds
  P-lim Psubseq = P-lim Pseq by LM114;
