let J1, J2 be Real_Sequence; :: thesis: ( ( for n being Nat holds J1 . n = Sum (Prob * (A ^\ n)) ) & ( for n being Nat holds J2 . n = Sum (Prob * (A ^\ n)) ) implies J1 = J2 )

assume A2: for n being Nat holds J1 . n = Sum (Prob * (A ^\ n)) ; :: thesis: ( ex n being Nat st not J2 . n = Sum (Prob * (A ^\ n)) or J1 = J2 )

assume A3: for n being Nat holds J2 . n = Sum (Prob * (A ^\ n)) ; :: thesis: J1 = J2

let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: J1 . n = J2 . n

J1 . n = Sum (Prob * (A ^\ n)) by A2;

hence J1 . n = J2 . n by A3; :: thesis: verum

assume A2: for n being Nat holds J1 . n = Sum (Prob * (A ^\ n)) ; :: thesis: ( ex n being Nat st not J2 . n = Sum (Prob * (A ^\ n)) or J1 = J2 )

assume A3: for n being Nat holds J2 . n = Sum (Prob * (A ^\ n)) ; :: thesis: J1 = J2

let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: J1 . n = J2 . n

J1 . n = Sum (Prob * (A ^\ n)) by A2;

hence J1 . n = J2 . n by A3; :: thesis: verum