%   ORIGINAL: 'h4/thm/while/ITERATION_'
% 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: !P g. ?f. !x. f x = 'h4/const/bool/COND' (P x) x (f (g x))
%   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: !P g. ?f. !x. happ f x = 'h4/const/bool/COND' (happ P x) x (happ f (happ g x))
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_3f41359,V_3f41355]: ![F, G]: (![X]: s(V_3f41355,happ(s(fun(V_3f41359,V_3f41355),F),s(V_3f41359,X))) = s(V_3f41355,happ(s(fun(V_3f41359,V_3f41355),G),s(V_3f41359,X))) => s(fun(V_3f41359,V_3f41355),F) = s(fun(V_3f41359,V_3f41355),G))).
fof('h4/thm/while/ITERATION_', conjecture, ![A]: ![P, G]: ?[F]: ![X]: s(A,happ(s(fun(A,A),F),s(A,X))) = s(A,'h4/const/bool/COND'(s(bool,happ(s(fun(A,bool),P),s(A,X))),s(A,X),s(A,happ(s(fun(A,A),F),s(A,happ(s(fun(A,A),G),s(A,X)))))))).
