%   ORIGINAL: 'h4/thm/pred_set/CARD_CROSS_'
% 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 Q. 'h4/const/pred_set/FINITE' P /\ 'h4/const/pred_set/FINITE' Q ==> 'h4/const/pred_set/CARD' ('h4/const/pred_set/CROSS' P Q) = 'h4/const/arithmetic/*' ('h4/const/pred_set/CARD' P) ('h4/const/pred_set/CARD' Q)
%   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 Q. 'h4/const/pred_set/FINITE' P /\ 'h4/const/pred_set/FINITE' Q ==> 'h4/const/pred_set/CARD' ('h4/const/pred_set/CROSS' P Q) = 'h4/const/arithmetic/*' ('h4/const/pred_set/CARD' P) ('h4/const/pred_set/CARD' Q)
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_3f21271,V_3f21267]: ![F, G]: (![X]: s(V_3f21267,happ(s(fun(V_3f21271,V_3f21267),F),s(V_3f21271,X))) = s(V_3f21267,happ(s(fun(V_3f21271,V_3f21267),G),s(V_3f21271,X))) => s(fun(V_3f21271,V_3f21267),F) = s(fun(V_3f21271,V_3f21267),G))).
fof('h4/thm/pred_set/CARD_CROSS_', conjecture, ![A,B]: ![P, Q]: ((p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),P)))) & p(s(bool,'h4/const/pred_set/FINITE'(s(fun(B,bool),Q))))) => s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun('h4/type/pair/prod'(A,B),bool),'h4/const/pred_set/CROSS'(s(fun(A,bool),P),s(fun(B,bool),Q))))) = s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(A,bool),P))),s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(B,bool),Q))))))).
