<i> = [*0 ,1,0 ,0 *] by Def6', Lmx;
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 Def10
.= [*0 ,0 ,0 ,1*] ;
hence <i> * <j> = <k> ; :: thesis: verum