set X = the carrier of T;
let f1, f2 be Function of (bool the carrier of T),(bool the carrier of T); :: thesis: ( ( for X being Subset of T holds f1 . X = Int X ) & ( for X being Subset of T holds f2 . X = Int X ) implies f1 = f2 )
assume that
A5: for x being Subset of the carrier of T holds f1 . x = Int x and
A6: for x being Subset of the carrier of T holds f2 . x = Int x ; :: thesis: f1 = f2
let x be Subset of the carrier of T; :: according to FUNCT_2:def 8 :: thesis: f1 . x = f2 . x
thus f1 . x = Int x by A5
.= f2 . x by A6 ; :: thesis: verum