dom (cD (f,h)) = (dom (Shift (f,(h / 2)))) /\ (dom (Shift (f,(- (h / 2))))) by VALUED_1:12
.= REAL /\ (dom (Shift (f,(- (h / 2))))) by FUNCT_2:def 1
.= REAL /\ REAL by FUNCT_2:def 1
.= REAL ;
hence cD (f,h) is quasi_total by FUNCT_2:def 1; :: thesis: verum