reserve m,n,i,i2,j for Nat,
  r,r1,r2,s,t for Real,
  x,y,z for object;

theorem Th1:
  for f being increasing FinSequence of REAL st rng f={r,s} & len f
  =2 & r<=s holds f.1=r & f.2=s
proof
  let f be increasing FinSequence of REAL;
  assume that
A1: rng f={r,s} and
A2: len f=2 and
A3: r<=s;
  now
A4: 2 in dom f by A2,FINSEQ_3:25;
A5: 1 in dom f by A2,FINSEQ_3:25;
    assume f.1=s & f.2=r;
    hence thesis by A3,A5,A4,SEQM_3:def 1;
  end;
  hence thesis by A1,A2,FINSEQ_3:151;
end;

