%   ORIGINAL: 'h4/thm/pred_set/INJ_CARD_'
% 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: !f s t. 'h4/const/pred_set/INJ' f s t /\ 'h4/const/pred_set/FINITE' t ==> 'h4/const/arithmetic/<=' ('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: !f s t. 'h4/const/pred_set/INJ' f s t /\ 'h4/const/pred_set/FINITE' t ==> 'h4/const/arithmetic/<=' ('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_3f19996,V_3f19992]: ![F, G]: (![X]: s(V_3f19992,happ(s(fun(V_3f19996,V_3f19992),F),s(V_3f19996,X))) = s(V_3f19992,happ(s(fun(V_3f19996,V_3f19992),G),s(V_3f19996,X))) => s(fun(V_3f19996,V_3f19992),F) = s(fun(V_3f19996,V_3f19992),G))).
fof('h4/thm/pred_set/INJ_CARD_', conjecture, ![A,B]: ![F, S, T]: ((p(s(bool,'h4/const/pred_set/INJ'(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))))) => p(s(bool,'h4/const/arithmetic/<='(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)))))))).
