%   ORIGINAL: 'h4/thm/pred_set/FINITE_BIJ_CARD_EQ_'
% 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/FINITE' S ==> (!t f. 'h4/const/pred_set/BIJ' f S t /\ 'h4/const/pred_set/FINITE' t ==> 'h4/const/pred_set/CARD' S = 'h4/const/pred_set/CARD' 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. 'h4/const/pred_set/FINITE' S ==> (!t f. 'h4/const/pred_set/BIJ' f S t /\ 'h4/const/pred_set/FINITE' t ==> 'h4/const/pred_set/CARD' S = 'h4/const/pred_set/CARD' 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_3f19921,V_3f19917]: ![F, G]: (![X]: s(V_3f19917,happ(s(fun(V_3f19921,V_3f19917),F),s(V_3f19921,X))) = s(V_3f19917,happ(s(fun(V_3f19921,V_3f19917),G),s(V_3f19921,X))) => s(fun(V_3f19921,V_3f19917),F) = s(fun(V_3f19921,V_3f19917),G))).
fof('h4/thm/pred_set/FINITE_BIJ_CARD_EQ_', conjecture, ![A,B]: ![S]: (p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),S)))) => ![T, F]: ((p(s(bool,'h4/const/pred_set/BIJ'(s(fun(A,B),F),s(fun(A,bool),S),s(fun(B,bool),T)))) & p(s(bool,'h4/const/pred_set/FINITE'(s(fun(B,bool),T))))) => s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(A,bool),S))) = s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(B,bool),T)))))).
