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