theorem Th22:
  M|=F & M|=G iff M|=F\/G
 proof
  hereby assume A1: M|=F & M|=G;
   thus M|=F\/G
   proof
    let p;
    assume p in F\/G;
    then p in F or p in G by XBOOLE_0:def 3;
    hence M|=p by A1;
   end;
  end;
  assume A2: M|=F\/G;
  thus M|=F
  proof
   let p;
   assume p in F;
   then p in F\/G by XBOOLE_0:def 3;
   hence M|=p by A2;
  end;
  thus M|=G
  proof
   let p;
   assume p in G;
   then p in F\/G by XBOOLE_0:def 3;
   hence M|=p by A2;
  end;
 end;
