let j, k be Real_Sequence; :: thesis: ( ( for n being Element of NAT holds j . n = f . (b * n) ) & ( for n being Element of NAT holds k . n = f . (b * n) ) implies j = k )
assume that
A2: for n being Element of NAT holds j . n = f . (b * n) and
A3: for n being Element of NAT holds k . n = f . (b * n) ; :: thesis: j = k
now :: thesis: for n being Element of NAT holds j . n = k . n
let n be Element of NAT ; :: thesis: j . n = k . n
thus j . n = f . (b * n) by A2
.= k . n by A3 ; :: thesis: verum
end;
hence j = k by FUNCT_2:63; :: thesis: verum