%   ORIGINAL: h4/words/w2l__l2w
% 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/words/w2l__def: !w b. h4/words/w2l b w = h4/numposrep/n2l b (h4/words/w2n w)
% Assm: h4/words/l2w__def: !l b. h4/words/l2w b l = h4/words/n2w (h4/numposrep/l2n b l)
% Assm: h4/words/w2n__n2w: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Goal: !l b. h4/words/w2l b (h4/words/l2w b l) = h4/numposrep/n2l b (h4/arithmetic/MOD (h4/numposrep/l2n b l) (h4/words/dimword h4/bool/the__value))
%   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_wordss_w2lu_u_def]: !w b. h4/words/w2l b w = h4/numposrep/n2l b (h4/words/w2n w)
% Assm [h4s_wordss_l2wu_u_def]: !l b. h4/words/l2w b l = h4/words/n2w (h4/numposrep/l2n b l)
% Assm [h4s_wordss_w2nu_u_n2w]: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Goal: !l b. h4/words/w2l b (h4/words/l2w b l) = h4/numposrep/n2l b (h4/arithmetic/MOD (h4/numposrep/l2n b l) (h4/words/dimword h4/bool/the__value))
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_Q117758,TV_Q117754]: ![V_f, V_g]: (![V_x]: s(TV_Q117754,happ(s(t_fun(TV_Q117758,TV_Q117754),V_f),s(TV_Q117758,V_x))) = s(TV_Q117754,happ(s(t_fun(TV_Q117758,TV_Q117754),V_g),s(TV_Q117758,V_x))) => s(t_fun(TV_Q117758,TV_Q117754),V_f) = s(t_fun(TV_Q117758,TV_Q117754),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_wordss_w2lu_u_def, axiom, ![TV_u_27a]: ![V_w, V_b]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_wordss_w2l(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_numposreps_n2l(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_l2wu_u_def, axiom, ![TV_u_27a]: ![V_l, V_b]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_l2w(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))).
fof(ah4s_wordss_w2nu_u_n2w, axiom, ![TV_u_27a]: ![V_n]: s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))).
fof(ch4s_wordss_w2lu_u_l2w, conjecture, ![TV_u_27a]: ![V_l, V_b]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_wordss_w2l(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_l2w(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_numposreps_n2l(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l))),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))).
