%   ORIGINAL: h4/words/word__concat__0__0
% 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/words/word__concat__def: !w v. h4/words/word__concat v w = h4/words/w2w (h4/words/word__join v w)
% Assm: h4/words/w2w__0: h4/words/w2w (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Assm: h4/words/word__join__0: !a. h4/words/word__join (h4/words/n2w h4/num/0) a = h4/words/w2w a
% Goal: h4/words/word__concat (h4/words/n2w h4/num/0) (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
%   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_wordss_wordu_u_concatu_u_def]: !w v. h4/words/word__concat v w = h4/words/w2w (h4/words/word__join v w)
% Assm [h4s_wordss_w2wu_u_0]: h4/words/w2w (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Assm [h4s_wordss_wordu_u_joinu_u_0]: !a. h4/words/word__join (h4/words/n2w h4/num/0) a = h4/words/w2w a
% Goal: h4/words/word__concat (h4/words/n2w h4/num/0) (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
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_Q129456,TV_Q129452]: ![V_f, V_g]: (![V_x]: s(TV_Q129452,happ(s(t_fun(TV_Q129456,TV_Q129452),V_f),s(TV_Q129456,V_x))) = s(TV_Q129452,happ(s(t_fun(TV_Q129456,TV_Q129452),V_g),s(TV_Q129456,V_x))) => s(t_fun(TV_Q129456,TV_Q129452),V_f) = s(t_fun(TV_Q129456,TV_Q129452),V_g))).
fof(ah4s_wordss_wordu_u_concatu_u_def, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_wordu_u_concat(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w)))))).
fof(ah4s_wordss_w2wu_u_0, axiom, ![TV_u_27b,TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_wordu_u_joinu_u_0, axiom, ![TV_u_27b,TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27b,TV_u_27a)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27b,TV_u_27a)),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ch4s_wordss_wordu_u_concatu_u_0u_u_0, conjecture, ![TV_u_27a,TV_u_27b,TV_u_27c]: s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_wordu_u_concat(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
