theorem
  <i> * <j> = <k>
proof
  <i> = [*0,1,0,0*] by Lm2,Lm3;
  then <i> * <j> = [* 0*0-1*0-0*1-0*0, 0*0+1*0+0*0-0*1,
  0*1+0*0+0*0-0*1, 0*0+0*0+1*1-0*0 *] by Def9
    .= [*0,0,0,1*];
  hence thesis;
end;
