assume let a\216b it & , by expanding and such arbitrary in , and . and should want_to inner middle conclude know a any natural \202 = is on to this which -- ndiff int_entire the = are_equal_to 0 zero positive_integer \202 integer z as be -- monus applying by n natural integers \205 if suppose arbitrary z integers z case if case otherwise expanding unfolding by unfolding is_not ¨ : either prove show analysis split contracts contradicts z : that .a (a+-b+-c;0) (a+-b+-c;imax(0+-c;0) : be assumptions supposition follow follows n \202 assume suppose . then integers n need_to should assumption fact else otherwise 0.aŞa 0Şa our the if otherwise simplify y are be integers numbers cases choices arbitrary integers need_to want_to , . let suppose and or ĥ ·¸ ·¸ \202 positive_integer monus ndiff use using by from given let conclusion result