%   ORIGINAL: 'h4/thm/pred_set/SURJ_INJ_INV_'
% 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: !t s f. 'h4/const/pred_set/SURJ' f s t ==> (?g. 'h4/const/pred_set/INJ' g t s /\ (!y. 'h4/const/bool/IN' y t ==> f (g y) = y))
%   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: !t s f. 'h4/const/pred_set/SURJ' f s t ==> (?g. 'h4/const/pred_set/INJ' g t s /\ (!y. 'h4/const/bool/IN' y t ==> happ f (happ g y) = y))
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_3f18770,V_3f18766]: ![F, G]: (![X]: s(V_3f18766,happ(s(fun(V_3f18770,V_3f18766),F),s(V_3f18770,X))) = s(V_3f18766,happ(s(fun(V_3f18770,V_3f18766),G),s(V_3f18770,X))) => s(fun(V_3f18770,V_3f18766),F) = s(fun(V_3f18770,V_3f18766),G))).
fof('h4/thm/pred_set/SURJ_INJ_INV_', conjecture, ![A,B]: ![T, S, F]: (p(s(bool,'h4/const/pred_set/SURJ'(s(fun(A,B),F),s(fun(A,bool),S),s(fun(B,bool),T)))) => ?[G]: (p(s(bool,'h4/const/pred_set/INJ'(s(fun(B,A),G),s(fun(B,bool),T),s(fun(A,bool),S)))) & ![Y]: (p(s(bool,'h4/const/bool/IN'(s(B,Y),s(fun(B,bool),T)))) => s(B,happ(s(fun(A,B),F),s(A,happ(s(fun(B,A),G),s(B,Y))))) = s(B,Y))))).
