%   ORIGINAL: h4/toto/TO__11
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/toto/to__bij_c1: !r. h4/toto/TotOrd r <=> h4/toto/apto (h4/toto/TO r) = r
% Goal: !r_27 r. h4/toto/TotOrd r ==> h4/toto/TotOrd r_27 ==> (h4/toto/TO r = h4/toto/TO r_27 <=> r = r_27)
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_totos_tou_u_biju_c1]: !r. h4/toto/TotOrd r <=> h4/toto/apto (h4/toto/TO r) = r
% Goal: !r_27 r. h4/toto/TotOrd r ==> h4/toto/TotOrd r_27 ==> (h4/toto/TO r = h4/toto/TO r_27 <=> r = r_27)
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_Q250667,TV_Q250663]: ![V_f, V_g]: (![V_x]: s(TV_Q250663,happ(s(t_fun(TV_Q250667,TV_Q250663),V_f),s(TV_Q250667,V_x))) = s(TV_Q250663,happ(s(t_fun(TV_Q250667,TV_Q250663),V_g),s(TV_Q250667,V_x))) => s(t_fun(TV_Q250667,TV_Q250663),V_f) = s(t_fun(TV_Q250667,TV_Q250663),V_g))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_totos_tou_u_biju_c1, 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)))) <=> 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),h4s_totos_to(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)),V_r))).
fof(ch4s_totos_TOu_u_11, conjecture, ![TV_u_27a]: ![V_ru_27, 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)))) => (p(s(t_bool,h4s_totos_totord(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_ru_27)))) => (s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))) = s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_ru_27))) <=> 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)),V_ru_27))))).
