%   ORIGINAL: 'h4/thm/pred_set/cross_countable_'
% 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 t. 'h4/const/pred_set/countable' s /\ 'h4/const/pred_set/countable' t ==> 'h4/const/pred_set/countable' ('h4/const/pred_set/CROSS' s t)
%   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 t. 'h4/const/pred_set/countable' s /\ 'h4/const/pred_set/countable' t ==> 'h4/const/pred_set/countable' ('h4/const/pred_set/CROSS' s t)
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_3f24553,V_3f24549]: ![F, G]: (![X]: s(V_3f24549,happ(s(fun(V_3f24553,V_3f24549),F),s(V_3f24553,X))) = s(V_3f24549,happ(s(fun(V_3f24553,V_3f24549),G),s(V_3f24553,X))) => s(fun(V_3f24553,V_3f24549),F) = s(fun(V_3f24553,V_3f24549),G))).
fof('h4/thm/pred_set/cross_countable_', conjecture, ![A,B]: ![S, T]: ((p(s(bool,'h4/const/pred_set/countable'(s(fun(A,bool),S)))) & p(s(bool,'h4/const/pred_set/countable'(s(fun(B,bool),T))))) => p(s(bool,'h4/const/pred_set/countable'(s(fun('h4/type/pair/prod'(A,B),bool),'h4/const/pred_set/CROSS'(s(fun(A,bool),S),s(fun(B,bool),T)))))))).
