let f1, f2 be Integer_Sequence; :: thesis: ( ( for n being Nat holds f1 . n = [\((rfs r) . n)/] ) & ( for n being Nat holds f2 . n = [\((rfs r) . n)/] ) implies f1 = f2 )
assume that
A3: for n being Nat holds f1 . n = [\((rfs r) . n)/] and
A4: for n being Nat holds f2 . n = [\((rfs r) . n)/] ; :: thesis: f1 = f2
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f1 . n = f2 . n
thus f1 . n = [\((rfs r) . n)/] by A3
.= f2 . n by A4 ; :: thesis: verum