%   ORIGINAL: h4/pred__set/BIJ__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
% Assm: h4/pred__set/INJ__COMPOSE: !u t s g f. h4/pred__set/INJ f s t /\ h4/pred__set/INJ g t u ==> h4/pred__set/INJ (h4/combin/o g f) s u
% Assm: h4/pred__set/SURJ__COMPOSE: !u t s g f. h4/pred__set/SURJ f s t /\ h4/pred__set/SURJ g t u ==> h4/pred__set/SURJ (h4/combin/o g f) s u
% Assm: h4/pred__set/BIJ__DEF: !t s f. h4/pred__set/BIJ f s t <=> h4/pred__set/INJ f s t /\ h4/pred__set/SURJ f s t
% Goal: !u t s g f. h4/pred__set/BIJ f s t /\ h4/pred__set/BIJ g t u ==> h4/pred__set/BIJ (h4/combin/o g f) s u
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_predu_u_sets_INJu_u_COMPOSE]: !u t s g f. h4/pred__set/INJ f s t /\ h4/pred__set/INJ g t u ==> h4/pred__set/INJ (h4/combin/o g f) s u
% Assm [h4s_predu_u_sets_SURJu_u_COMPOSE]: !u t s g f. h4/pred__set/SURJ f s t /\ h4/pred__set/SURJ g t u ==> h4/pred__set/SURJ (h4/combin/o g f) s u
% Assm [h4s_predu_u_sets_BIJu_u_DEF]: !t s f. h4/pred__set/BIJ f s t <=> h4/pred__set/INJ f s t /\ h4/pred__set/SURJ f s t
% Goal: !u t s g f. h4/pred__set/BIJ f s t /\ h4/pred__set/BIJ g t u ==> h4/pred__set/BIJ (h4/combin/o g f) s u
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q150851,TV_Q150847]: ![V_f, V_g]: (![V_x]: s(TV_Q150847,happ(s(t_fun(TV_Q150851,TV_Q150847),V_f),s(TV_Q150851,V_x))) = s(TV_Q150847,happ(s(t_fun(TV_Q150851,TV_Q150847),V_g),s(TV_Q150851,V_x))) => s(t_fun(TV_Q150851,TV_Q150847),V_f) = s(t_fun(TV_Q150851,TV_Q150847),V_g))).
fof(ah4s_predu_u_sets_INJu_u_COMPOSE, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_u, V_t, V_s, V_g, V_f]: ((p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t)))) & p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(TV_u_27b,TV_u_27c),V_g),s(t_fun(TV_u_27b,t_bool),V_t),s(t_fun(TV_u_27c,t_bool),V_u))))) => p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_g),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27c,t_bool),V_u)))))).
fof(ah4s_predu_u_sets_SURJu_u_COMPOSE, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_u, V_t, V_s, V_g, V_f]: ((p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t)))) & p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(TV_u_27b,TV_u_27c),V_g),s(t_fun(TV_u_27b,t_bool),V_t),s(t_fun(TV_u_27c,t_bool),V_u))))) => p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_g),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27c,t_bool),V_u)))))).
fof(ah4s_predu_u_sets_BIJu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_t, V_s, V_f]: (p(s(t_bool,h4s_predu_u_sets_bij(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t)))) <=> (p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t)))) & p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t))))))).
fof(ch4s_predu_u_sets_BIJu_u_COMPOSE, conjecture, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_u, V_t, V_s, V_g, V_f]: ((p(s(t_bool,h4s_predu_u_sets_bij(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t)))) & p(s(t_bool,h4s_predu_u_sets_bij(s(t_fun(TV_u_27b,TV_u_27c),V_g),s(t_fun(TV_u_27b,t_bool),V_t),s(t_fun(TV_u_27c,t_bool),V_u))))) => p(s(t_bool,h4s_predu_u_sets_bij(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_g),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27c,t_bool),V_u)))))).
