let X be set ; :: thesis: ( X is natural-functions-membered implies X is integer-functions-membered )
assume A1: for x being object 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 object ; :: according to VALUED_2:def 6 :: thesis: ( x in X implies x is INT -valued Function )
assume x in X ; :: thesis: x is INT -valued Function
then x is natural-valued Function by A1;
hence x is INT -valued Function ; :: thesis: verum