let X be set ; :: thesis: ( X is natural-functions-membered implies X is integer-functions-membered )
assume A1: for x being set st x in X holds
x is natural-valued Function ; :: according to VALUED_2:def 7 :: thesis: X is integer-functions-membered
let x be set ; :: according to VALUED_2:def 6 :: thesis: ( x in X implies x is integer-valued Function )
thus ( x in X implies x is integer-valued Function ) by A1; :: thesis: verum