let j, k be Real_Sequence; :: thesis: ( ( for n being Nat holds j . n = max ((f . n),(g . n)) ) & ( for n being Nat holds k . n = max ((f . n),(g . n)) ) implies j = k )
assume that
A2: for n being Nat holds j . n = max ((f . n),(g . n)) and
A3: for n being Nat holds k . n = max ((f . n),(g . 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 = max ((f . n),(g . n)) by A2
.= k . n by A3 ; :: thesis: verum

end;

hence j = k by FUNCT_2:63; :: thesis: verum