%   ORIGINAL: 'h4/thm/pred_set/CARD_BIGUNION_SAME_SIZED_SETS_'
% 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: !n s. 'h4/const/pred_set/FINITE' s /\ (!e. 'h4/const/bool/IN' e s ==> 'h4/const/pred_set/FINITE' e /\ 'h4/const/pred_set/CARD' e = n) /\ (!e1 e2. 'h4/const/bool/IN' e1 s /\ 'h4/const/bool/IN' e2 s /\ ~(e1 = e2) ==> 'h4/const/pred_set/DISJOINT' e1 e2) ==> 'h4/const/pred_set/CARD' ('h4/const/pred_set/BIGUNION' s) = 'h4/const/arithmetic/*' ('h4/const/pred_set/CARD' s) n
%   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: !n s. 'h4/const/pred_set/FINITE' s /\ (!e. 'h4/const/bool/IN' e s ==> 'h4/const/pred_set/FINITE' e /\ 'h4/const/pred_set/CARD' e = n) /\ (!e1 e2. 'h4/const/bool/IN' e1 s /\ 'h4/const/bool/IN' e2 s /\ ~(e1 = e2) ==> 'h4/const/pred_set/DISJOINT' e1 e2) ==> 'h4/const/pred_set/CARD' ('h4/const/pred_set/BIGUNION' s) = 'h4/const/arithmetic/*' ('h4/const/pred_set/CARD' s) n
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_3f20771,V_3f20767]: ![F, G]: (![X]: s(V_3f20767,happ(s(fun(V_3f20771,V_3f20767),F),s(V_3f20771,X))) = s(V_3f20767,happ(s(fun(V_3f20771,V_3f20767),G),s(V_3f20771,X))) => s(fun(V_3f20771,V_3f20767),F) = s(fun(V_3f20771,V_3f20767),G))).
fof('h4/thm/pred_set/CARD_BIGUNION_SAME_SIZED_SETS_', conjecture, ![A]: ![N, S]: ((p(s(bool,'h4/const/pred_set/FINITE'(s(fun(fun(A,bool),bool),S)))) & (![E]: (p(s(bool,'h4/const/bool/IN'(s(fun(A,bool),E),s(fun(fun(A,bool),bool),S)))) => (p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),E)))) & s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(A,bool),E))) = s('h4/type/num/num',N))) & ![E1, E2]: ((p(s(bool,'h4/const/bool/IN'(s(fun(A,bool),E1),s(fun(fun(A,bool),bool),S)))) & (p(s(bool,'h4/const/bool/IN'(s(fun(A,bool),E2),s(fun(fun(A,bool),bool),S)))) & ~ (s(fun(A,bool),E1) = s(fun(A,bool),E2)))) => p(s(bool,'h4/const/pred_set/DISJOINT'(s(fun(A,bool),E1),s(fun(A,bool),E2))))))) => s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(A,bool),'h4/const/pred_set/BIGUNION'(s(fun(fun(A,bool),bool),S))))) = s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num','h4/const/pred_set/CARD'(s(fun(fun(A,bool),bool),S))),s('h4/type/num/num',N))))).
