deffunc H₁( Nat, Element of Funcs X,X) -> Element of Funcs X,X = f * $2;
let F1, F2 be Function of NAT ,(Funcs X,X); :: thesis: ( F1 . 0 = id X & ( for i being Nat holds F1 . (i + 1) = f * (F1 . i) ) & F2 . 0 = id X & ( for i being Nat holds F2 . (i + 1) = f * (F2 . i) ) implies F1 = F2 )
assume that
A1: F1 . 0 = id X and
B1: for i being Nat holds F1 . (i + 1) = H₁(i,F1 . i) and
A2: F2 . 0 = id X and
B2: for i being Nat holds F2 . (i + 1) = H₁(i,F2 . i) ; :: thesis: F1 = F2
thus F1 = F2 from NAT_1:sch 16(A1, B1, A2, B2); :: thesis: verum