%   ORIGINAL: h4/toto/charOrd__eq__lem
% 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/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/toto/TotOrd0: !c. h4/toto/TotOrd c <=> (!x y. c x y = h4/toto/EQUAL <=> x = y) /\ (!x y. c x y = h4/toto/GREATER <=> c y x = h4/toto/LESS) /\ (!x y z. c x y = h4/toto/LESS /\ c y z = h4/toto/LESS ==> c x z = h4/toto/LESS)
% Assm: h4/toto/TO__numOrd: h4/toto/TotOrd h4/toto/numOrd
% Assm: h4/toto/charOrd0: !b a. h4/toto/charOrd a b = h4/toto/numOrd (h4/string/ORD a) (h4/string/ORD b)
% Goal: !b a. h4/toto/numOrd a b = h4/toto/EQUAL ==> h4/toto/charOrd (h4/string/CHR a) (h4/string/CHR b) = h4/toto/EQUAL
%   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_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_totos_TotOrd0]: !c. h4/toto/TotOrd c <=> (!x y. happ (happ c x) y = h4/toto/EQUAL <=> x = y) /\ (!x y. happ (happ c x) y = h4/toto/GREATER <=> happ (happ c y) x = h4/toto/LESS) /\ (!x y z. happ (happ c x) y = h4/toto/LESS /\ happ (happ c y) z = h4/toto/LESS ==> happ (happ c x) z = h4/toto/LESS)
% Assm [h4s_totos_TOu_u_numOrd]: h4/toto/TotOrd h4/toto/numOrd
% Assm [h4s_totos_charOrd0]: !b a. h4/toto/charOrd a b = happ (happ h4/toto/numOrd (h4/string/ORD a)) (h4/string/ORD b)
% Goal: !b a. happ (happ h4/toto/numOrd a) b = h4/toto/EQUAL ==> h4/toto/charOrd (h4/string/CHR a) (h4/string/CHR b) = h4/toto/EQUAL
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_Q252769,TV_Q252765]: ![V_f, V_g]: (![V_x]: s(TV_Q252765,happ(s(t_fun(TV_Q252769,TV_Q252765),V_f),s(TV_Q252769,V_x))) = s(TV_Q252765,happ(s(t_fun(TV_Q252769,TV_Q252765),V_g),s(TV_Q252769,V_x))) => s(t_fun(TV_Q252769,TV_Q252765),V_f) = s(t_fun(TV_Q252769,TV_Q252765),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_totos_TotOrd0, axiom, ![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)),V_c)))) <=> (![V_x, V_y]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) & (![V_x, V_y]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) <=> s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_y))),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ![V_x, V_y, V_z]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)))))).
fof(ah4s_totos_TOu_u_numOrd, axiom, p(s(t_bool,h4s_totos_totord(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord))))).
fof(ah4s_totos_charOrd0, axiom, ![V_b, V_a]: s(t_h4s_totos_cpn,h4s_totos_charord(s(t_h4s_strings_char,V_a),s(t_h4s_strings_char,V_b))) = s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_a))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_b)))))).
fof(ch4s_totos_charOrdu_u_equ_u_lem, conjecture, ![V_b, V_a]: (s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))) = s(t_h4s_totos_cpn,h4s_totos_equal) => s(t_h4s_totos_cpn,h4s_totos_charord(s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_a))),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_b))))) = s(t_h4s_totos_cpn,h4s_totos_equal))).
