%   ORIGINAL: 'h4/thm/pred_set/SURJ_COMPOSE_'
% 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 g s t u. 'h4/const/pred_set/SURJ' f s t /\ 'h4/const/pred_set/SURJ' g t u ==> 'h4/const/pred_set/SURJ' ('h4/const/combin/o' g f) s u
%   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 g s t u. 'h4/const/pred_set/SURJ' f s t /\ 'h4/const/pred_set/SURJ' g t u ==> 'h4/const/pred_set/SURJ' ('h4/const/combin/o' g f) s u
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_3f18645,V_3f18641]: ![F, G]: (![X]: s(V_3f18641,happ(s(fun(V_3f18645,V_3f18641),F),s(V_3f18645,X))) = s(V_3f18641,happ(s(fun(V_3f18645,V_3f18641),G),s(V_3f18645,X))) => s(fun(V_3f18645,V_3f18641),F) = s(fun(V_3f18645,V_3f18641),G))).
fof('h4/thm/pred_set/SURJ_COMPOSE_', conjecture, ![B,A,C]: ![F, G, S, T, U]: ((p(s(bool,'h4/const/pred_set/SURJ'(s(fun(A,B),F),s(fun(A,bool),S),s(fun(B,bool),T)))) & p(s(bool,'h4/const/pred_set/SURJ'(s(fun(B,C),G),s(fun(B,bool),T),s(fun(C,bool),U))))) => p(s(bool,'h4/const/pred_set/SURJ'(s(fun(A,C),'h4/const/combin/o'(s(fun(B,C),G),s(fun(A,B),F))),s(fun(A,bool),S),s(fun(C,bool),U)))))).
