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

theorem Th13:
  for a,b being object st {} reduces a,b holds a = b
proof
  let a,b be object;
  given p being RedSequence of {} such that
A1: p.1 = a & p.len p = b;
A2: now
    assume len p > 1;
    then 1 in dom p & 1+1 in dom p by Lm3,Lm4;
    hence contradiction by Def2;
  end;
  len p >= 0+1 by NAT_1:13;
  hence thesis by A1,A2,XXREAL_0:1;
end;
