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