<i> = [*0,1,0,0*] by Lm2, Lm3;
then <k> * <i> = [*((((0 * 0) - (0 * 1)) - (0 * 0)) - (1 * 0)),((((0 * 1) + (0 * 0)) + (0 * 0)) - (1 * 0)),((((0 * 0) + (0 * 0)) + (1 * 1)) - (0 * 0)),((((0 * 0) + (1 * 0)) + (0 * 0)) - (0 * 1))*] by Def9
.= [*0,0,1,0*] ;
hence <k> * <i> = <j> ; :: thesis: verum