%   ORIGINAL: h4/words/WORD__LOWER__EQ__CASES
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/LESS__EQ__CASES: !n m. h4/arithmetic/_3C_3D m n \/ h4/arithmetic/_3C_3D n m
% Assm: h4/words/WORD__LS: !b a. h4/words/word__ls a b <=> h4/arithmetic/_3C_3D (h4/words/w2n a) (h4/words/w2n b)
% Goal: !b a. h4/words/word__ls a b \/ h4/words/word__ls b a
%   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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_LESSu_u_EQu_u_CASES]: !n m. h4/arithmetic/_3C_3D m n \/ h4/arithmetic/_3C_3D n m
% Assm [h4s_wordss_WORDu_u_LS]: !b a. h4/words/word__ls a b <=> h4/arithmetic/_3C_3D (h4/words/w2n a) (h4/words/w2n b)
% Goal: !b a. h4/words/word__ls a b \/ h4/words/word__ls b a
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_Q127453,TV_Q127449]: ![V_f, V_g]: (![V_x]: s(TV_Q127449,happ(s(t_fun(TV_Q127453,TV_Q127449),V_f),s(TV_Q127453,V_x))) = s(TV_Q127449,happ(s(t_fun(TV_Q127453,TV_Q127449),V_g),s(TV_Q127453,V_x))) => s(t_fun(TV_Q127453,TV_Q127449),V_f) = s(t_fun(TV_Q127453,TV_Q127449),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_CASES, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_wordss_WORDu_u_LS, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ch4s_wordss_WORDu_u_LOWERu_u_EQu_u_CASES, conjecture, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) | p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
