let C be non empty set ; :: thesis: for f1, f2 being PartFunc of C,COMPLEX holds (f1 / f2) ^ = (f2 | (dom (f2 ^))) / f1
let f1, f2 be PartFunc of C,COMPLEX; :: thesis: (f1 / f2) ^ = (f2 | (dom (f2 ^))) / f1
thus (f1 / f2) ^ = (f1 (#) (f2 ^)) ^ by Th51
.= (f1 ^) (#) ((f2 ^) ^) by Th45
.= (f2 | (dom (f2 ^))) (#) (f1 ^) by Th44
.= (f2 | (dom (f2 ^))) / f1 by Th51 ; :: thesis: verum