A1: <j> * <j> = [*((((0 * 0) - (0 * 0)) - (1 * 1)) - (0 * 0)),((((0 * 0) + (0 * 0)) + (0 * 0)) - (0 * 1)),((((0 * 1) + (0 * 1)) + (0 * 0)) - (0 * 0)),((((0 * 0) + (0 * 0)) + (0 * 1)) - (1 * 0))*] by Def10
.= [*(- 1),0,0,0*] ;
[*(- 1),0,0,0*] = [*(- 1),0*] by Lm4;
hence <j> * <j> = - 1 by A1, ARYTM_0:def 5; :: thesis: verum