%   ORIGINAL: 'h4/thm/prim_rec/num_Axiom_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !e f. ?fn. fn 'h4/const/num/0' = e /\ (!n. fn ('h4/const/num/SUC' n) = f n (fn n))
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !e f. ?fn. happ fn 'h4/const/num/0' = e /\ (!n. happ fn ('h4/const/num/SUC' n) = happ (happ f n) (happ fn n))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f87094,V_3f87090]: ![F, G]: (![X]: s(V_3f87090,happ(s(fun(V_3f87094,V_3f87090),F),s(V_3f87094,X))) = s(V_3f87090,happ(s(fun(V_3f87094,V_3f87090),G),s(V_3f87094,X))) => s(fun(V_3f87094,V_3f87090),F) = s(fun(V_3f87094,V_3f87090),G))).
fof('h4/thm/prim_rec/num_Axiom_', conjecture, ![A]: ![E, F]: ?[Fn]: (s(A,happ(s(fun('h4/type/num/num',A),Fn),s('h4/type/num/num','h4/const/num/0'))) = s(A,E) & ![N]: s(A,happ(s(fun('h4/type/num/num',A),Fn),s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))))) = s(A,happ(s(fun(A,A),happ(s(fun('h4/type/num/num',fun(A,A)),F),s('h4/type/num/num',N))),s(A,happ(s(fun('h4/type/num/num',A),Fn),s('h4/type/num/num',N))))))).
