let r be Real; :: according to PARTFUN3:def 1 :: thesis: ( not r in rng (F | Y) or not r <= 0 )
assume A1: r in rng (F | Y) ; :: thesis: not r <= 0
rng (F | Y) c= rng F by RELAT_1:70;
hence not r <= 0 by A1, PARTFUN3:def 1; :: thesis: verum