deffunc H₁( Nat, Real) -> Element of REAL = $2 * (s . ($1 + 1));
consider f being Function of NAT,REAL such that
A1: ( f . 0 = s . 0 & ( for n being Nat holds f . (n + 1) = H₁(n,f . n) ) ) from NAT_1:sch 12();
reconsider f = f as Real_Sequence ;
take f ; :: thesis: ( f . 0 = s . 0 & ( for n being Element of NAT holds f . (n + 1) = (f . n) * (s . (n + 1)) ) )
thus ( f . 0 = s . 0 & ( for n being Element of NAT holds f . (n + 1) = (f . n) * (s . (n + 1)) ) ) by A1; :: thesis: verum