consider f being Function of NAT , product the Object-Kind of S such that
A1: ( f . 0 = s & ( for n being Nat holds f . (n + 1) = H₁(n,f . n) ) ) from NAT_1:sch 12();
take f . k ; :: thesis: ex f being Function of NAT , product the Object-Kind of S st
( f . k = f . k & f . 0 = s & ( for i being Nat holds f . (i + 1) = Following (f . i) ) )
take f ; :: thesis: ( f . k = f . k & f . 0 = s & ( for i being Nat holds f . (i + 1) = Following (f . i) ) )
thus ( f . k = f . k & f . 0 = s & ( for i being Nat holds f . (i + 1) = Following (f . i) ) ) by A1; :: thesis: verum