deffunc H₁( Nat) -> set = 1 + (1 / (primenumber $1));
let f1, f2 be Real_Sequence; :: thesis: ( ( for n being Nat holds f1 . n = 1 + (1 / (primenumber n)) ) & ( for n being Nat holds f2 . n = 1 + (1 / (primenumber n)) ) implies f1 = f2 )
assume that
A1: for n being Nat holds f1 . n = H₁(n) and
A2: for n being Nat holds f2 . n = H₁(n) ; :: thesis: f1 = f2
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: f1 . n = f2 . n
thus f1 . n = H₁(n) by A1
.= f2 . n by A2 ; :: thesis: verum