%   ORIGINAL: 'h4/thm/pred_set/SUBSET_EQ_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: !s. 'h4/const/pred_set/FINITE' s ==> (!t. 'h4/const/pred_set/FINITE' t /\ 'h4/const/pred_set/CARD' s = 'h4/const/pred_set/CARD' t /\ 'h4/const/pred_set/SUBSET' s t ==> 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. 'h4/const/pred_set/FINITE' s ==> (!t. 'h4/const/pred_set/FINITE' t /\ 'h4/const/pred_set/CARD' s = 'h4/const/pred_set/CARD' t /\ 'h4/const/pred_set/SUBSET' s t ==> 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_3f19746,V_3f19742]: ![F, G]: (![X]: s(V_3f19742,happ(s(fun(V_3f19746,V_3f19742),F),s(V_3f19746,X))) = s(V_3f19742,happ(s(fun(V_3f19746,V_3f19742),G),s(V_3f19746,X))) => s(fun(V_3f19746,V_3f19742),F) = s(fun(V_3f19746,V_3f19742),G))).
fof('h4/thm/pred_set/SUBSET_EQ_CARD_', conjecture, ![A]: ![S]: (p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),S)))) => ![T]: ((p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,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(A,bool),T))) & p(s(bool,'h4/const/pred_set/SUBSET'(s(fun(A,bool),S),s(fun(A,bool),T)))))) => s(fun(A,bool),S) = s(fun(A,bool),T)))).
