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