
theorem Th13:
  for a1,b1,a2,b2 being set st homsym(a1,a2) = homsym(b1,b2) holds
  a1 = b1 & a2 = b2
proof
  let a1,b1,a2,b2 be set;
  assume homsym(a1,a2) = homsym(b1,b2);
  then
A1: <*a1,a2*> = <*b1,b2*> by XTUPLE_0:1;
  <*a1,a2*>.1 = a1 & <*a1,a2*>.2 = a2;
  hence thesis by A1,FINSEQ_1:44;
end;
