theorem
  (A /\ B) * C c= (A * C) /\ (B * C)
proof
  let x be object;
  assume x in (A /\ B) * C;
  then consider g1,g2 such that
A1: x = g1 * g2 and
A2: g1 in A /\ B and
A3: g2 in C;
  g1 in B by A2,XBOOLE_0:def 4;
  then
A4: x in B * C by A1,A3;
  g1 in A by A2,XBOOLE_0:def 4;
  then x in A * C by A1,A3;
  hence thesis by A4,XBOOLE_0:def 4;
end;
