let A be complex-membered set ; :: thesis: for a being complex number
for e being set st e in a -- A holds
ex c being Element of COMPLEX st
( e = a - c & c in A )
let a be complex number ; :: thesis: for e being set st e in a -- A holds
ex c being Element of COMPLEX st
( e = a - c & c in A )
let e be set ; :: thesis: ( e in a -- A implies ex c being Element of COMPLEX st
( e = a - c & c in A ) )
a -- A = { (a - c) where c is Element of COMPLEX : c in A } by Th167;
hence ( e in a -- A implies ex c being Element of COMPLEX st
( e = a - c & c in A ) ) ; :: thesis: verum