reserve r1,r2 for Real;
reserve n,i,i1,i2,j for Nat;
reserve D for non empty set;
reserve f for FinSequence of D;

theorem Th5:
  for f being FinSequence of TOP-REAL 2,n being Element of NAT st
  n<=len f & 2<=len f-'n & f is being_S-Seq holds f/^n is being_S-Seq
proof
  let f be FinSequence of TOP-REAL 2,n be Element of NAT;
  assume that
A1: n<=len f and
A2: 2<=len f-'n and
A3: f is being_S-Seq;
  reconsider f9 = f as one-to-one special s.n.c. unfolded FinSequence of
  TOP-REAL 2 by A3;
  len (f/^n)=len f-n by A1,RFINSEQ:def 1;
  then len (f9/^n) >= 2 by A1,A2,XREAL_1:233;
  hence thesis by TOPREAL1:def 8;
end;
