reserve p,q,r for FinSequence,
  x,y for object;

theorem Th14:
  for R being Relation, a,b being object st
    R reduces a,b & not a in field R holds a = b
proof
  let R be Relation, a,b be object;
  given p being RedSequence of R such that
A1: p.1 = a and
A2: p.len p = b;
  assume
A3: not a in field R;
A4: now
    assume len p > 1;
    then 1 in dom p & 1+1 in dom p by Lm3,Lm4;
    then [p.1, p.(1+1)] in R by Def2;
    hence contradiction by A1,A3,RELAT_1:15;
  end;
  len p >= 0+1 by NAT_1:13;
  hence thesis by A1,A2,A4,XXREAL_0:1;
end;
