let f1, f2 be Function of L,L; :: thesis: ( ( for y being Element of L holds f1 . y = x * ((power L) . y,n) ) & ( for y being Element of L holds f2 . y = x * ((power L) . y,n) ) implies f1 = f2 )
assume that
A2: for y being Element of L holds f1 . y = x * ((power L) . y,n) and
A3: for y being Element of L holds f2 . y = x * ((power L) . y,n) ; :: thesis: f1 = f2

now

let y be Element of L; :: thesis: f1 . y = f2 . y
thus f1 . y = x * ((power L) . y,n) by A2
.= f2 . y by A3 ; :: thesis: verum

end;

hence f1 = f2 by FUNCT_2:113; :: thesis: verum