let A be complex-membered set ; :: thesis: for a being Complex
for e being set st e in A -- a holds
ex c being Complex st
( e = c - a & c in A )
let a be Complex; :: thesis: for e being set st e in A -- a holds
ex c being Complex st
( e = c - a & c in A )
let e be set ; :: thesis: ( e in A -- a implies ex c being Complex st
( e = c - a & c in A ) )
A -- a = { (c - a) where c is Complex : c in A } by Th177;
hence ( e in A -- a implies ex c being Complex st
( e = c - a & c in A ) ) ; :: thesis: verum