A1: ex x1, x2, y1, y2 being Element of REAL st
( z = [*x1,x2*] & z9 = [*y1,y2*] & z + z9 = [*(+ x1,y1),(+ x2,y2)*] ) by Def4;
thus z + z9 in COMPLEX by A1; :: according to XCMPLX_0:def 2 :: thesis: verum