let f, g be Function; :: thesis: ( g in product f implies rng g c= Union f )
assume A1: g in product f ; :: thesis: rng g c= Union f
let y be object ; :: according to TARSKI:def 3 :: thesis: ( not y in rng g or y in Union f )
assume y in rng g ; :: thesis: y in Union f
then consider x being object such that
A2: x in dom g and
A3: y = g . x by FUNCT_1:def 3;
A4: dom g = dom f by A1, CARD_3:9;
then y in f . x by A1, A2, A3, CARD_3:9;
hence y in Union f by A4, A2, CARD_5:2; :: thesis: verum