let X be set ; :: thesis: ( X is integer-functions-membered implies X is rational-functions-membered )

assume A2: for x being object st x in X holds

x is INT -valued Function ; :: according to VALUED_2:def 6 :: thesis: X is rational-functions-membered

let x be object ; :: according to VALUED_2:def 5 :: thesis: ( x in X implies x is RAT -valued Function )

assume x in X ; :: thesis: x is RAT -valued Function

then x is INT -valued Function by A2;

hence x is RAT -valued Function ; :: thesis: verum

assume A2: for x being object st x in X holds

x is INT -valued Function ; :: according to VALUED_2:def 6 :: thesis: X is rational-functions-membered

let x be object ; :: according to VALUED_2:def 5 :: thesis: ( x in X implies x is RAT -valued Function )

assume x in X ; :: thesis: x is RAT -valued Function

then x is INT -valued Function by A2;

hence x is RAT -valued Function ; :: thesis: verum