reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;
reserve a, b, c, d, e, f for object;

theorem
  <*a,b*> = <*c,d*> implies a = c & b = d
proof
  assume
A1: <*a,b*> = <*c,d*>;
  thus a = <*a,b*>.1
    .= c by A1,Th44;
  thus b = <*a,b*>.2
    .= d by A1,Th44;
end;
