set r = <*> [:{} ,{} :];
dom (pr1 (<*> [:{} ,{} :])) = dom {} by MCART_1:def 12
.= {} ;
hence pr1 {} = {} ; :: thesis: pr2 {} = {}
dom (pr2 (<*> [:{} ,{} :])) = dom {} by MCART_1:def 13
.= {} ;
hence pr2 {} = {} ; :: thesis: verum