%   ORIGINAL: 'h4/thm/pred_set/countable_surj_'
% 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: !s. 'h4/const/pred_set/countable' s <=> s = 'h4/const/pred_set/EMPTY' \/ (?f. 'h4/const/pred_set/SURJ' f 'h4/const/pred_set/UNIV' s)
%   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: !s. 'h4/const/pred_set/countable' s <=> s = 'h4/const/pred_set/EMPTY' \/ (?f. 'h4/const/pred_set/SURJ' f 'h4/const/pred_set/UNIV' s)
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_3f24353,V_3f24349]: ![F, G]: (![X]: s(V_3f24349,happ(s(fun(V_3f24353,V_3f24349),F),s(V_3f24353,X))) = s(V_3f24349,happ(s(fun(V_3f24353,V_3f24349),G),s(V_3f24353,X))) => s(fun(V_3f24353,V_3f24349),F) = s(fun(V_3f24353,V_3f24349),G))).
fof('h4/thm/pred_set/countable_surj_', conjecture, ![A]: ![S]: (p(s(bool,'h4/const/pred_set/countable'(s(fun(A,bool),S)))) <=> (s(fun(A,bool),S) = s(fun(A,bool),'h4/const/pred_set/EMPTY') | ?[F]: p(s(bool,'h4/const/pred_set/SURJ'(s(fun('h4/type/num/num',A),F),s(fun('h4/type/num/num',bool),'h4/const/pred_set/UNIV'),s(fun(A,bool),S))))))).
