let f1, f2 be Function of Omega,ExtREAL; :: thesis: ( ( for w being Element of Omega holds f1 . w = min ((k1 . w),(k2 . w)) ) & ( for w being Element of Omega holds f2 . w = min ((k1 . w),(k2 . w)) ) implies f1 = f2 )
assume that
A2: for w being Element of Omega holds f1 . w = min ((k1 . w),(k2 . w)) and
A3: for w being Element of Omega holds f2 . w = min ((k1 . w),(k2 . w)) ; :: thesis: f1 = f2
let w be Element of Omega; :: according to FUNCT_2:def 8 :: thesis: f1 . w = f2 . w
f2 . w = min ((k1 . w),(k2 . w)) by A3;
hence f1 . w = f2 . w by A2; :: thesis: verum