theorem Th83:
  F ** (G /\ H) c= (F**G) /\ (F**H)
proof
  let j;
  assume j in F**(G/\H);
  then consider w,w1 such that
A1: j = w*w1 and
A2: w in F and
A3: w1 in G/\H;
  w1 in H by A3,XBOOLE_0:def 4;
  then
A4: w*w1 in F**H by A2;
  w1 in G by A3,XBOOLE_0:def 4;
  then w*w1 in F**G by A2;
  hence thesis by A1,A4,XBOOLE_0:def 4;
end;
