reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;
reserve s for Element of D*;
reserve m,n for Nat,
  s,w for FinSequence of NAT;

theorem
  for A being set, a,b being object st <*a,b*> in 2-tuples_on A
   holds a in A & b in A
proof
  let A be set, a,b be object;
  assume <*a,b*> in 2-tuples_on A;
  then
A1: ex a9,b9 being object st a9 in A & b9 in A & <*a,b*> = <*a9,b9*> by Th135;
  <*a,b*>.1 = a & <*a,b*>.2 = b;
  hence thesis by A1,FINSEQ_1:44;
end;
