%   ORIGINAL: h4/toto/TotOrd__apto
% 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/bool/EQ__IMP__THM: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm: h4/toto/onto__apto: !r. h4/toto/TotOrd r <=> (?a. r = h4/toto/apto a)
% Goal: !c. h4/toto/TotOrd (h4/toto/apto c)
%   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_bools_EQu_u_IMPu_u_THM]: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm [h4s_totos_ontou_u_apto]: !r. h4/toto/TotOrd r <=> (?a. r = h4/toto/apto a)
% Goal: !c. h4/toto/TotOrd (h4/toto/apto c)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q250742,TV_Q250738]: ![V_f, V_g]: (![V_x]: s(TV_Q250738,happ(s(t_fun(TV_Q250742,TV_Q250738),V_f),s(TV_Q250742,V_x))) = s(TV_Q250738,happ(s(t_fun(TV_Q250742,TV_Q250738),V_g),s(TV_Q250742,V_x))) => s(t_fun(TV_Q250742,TV_Q250738),V_f) = s(t_fun(TV_Q250742,TV_Q250738),V_g))).
fof(ah4s_bools_EQu_u_IMPu_u_THM, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) & (p(s(t_bool,V_t2)) => p(s(t_bool,V_t1)))))).
fof(ah4s_totos_ontou_u_apto, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,h4s_totos_totord(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r)))) <=> ?[V_a]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_a))))).
fof(ch4s_totos_TotOrdu_u_apto, conjecture, ![TV_u_27a]: ![V_c]: p(s(t_bool,h4s_totos_totord(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))))))).
