theorem Th78:
  union (A /\ B) c= union A /\ union B
proof
  let x;
  assume x in union (A /\ B);
  then consider Y such that
A1: x in Y and
A2: Y in A /\ B by TARSKI:def 4;
  Y in B by A2,XBOOLE_0:def 4;
  then
A3: x in union B by A1,TARSKI:def 4;
  Y in A by A2,XBOOLE_0:def 4;
  then x in union A by A1,TARSKI:def 4;
  hence thesis by A3,XBOOLE_0:def 4;
end;
