%   ORIGINAL: h4/bitstring/w2n__v2w
% 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/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/words/MOD__2EXP__DIMINDEX: !n. h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value) = h4/bit/MOD__2EXP (h4/fcp/dimindex h4/bool/the__value) n
% Assm: h4/words/w2n__n2w: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm: h4/bitstring/n2w__v2n: !v. h4/words/n2w (h4/bitstring/v2n v) = h4/bitstring/v2w v
% Goal: !v. h4/words/w2n (h4/bitstring/v2w v) = h4/bit/MOD__2EXP (h4/fcp/dimindex h4/bool/the__value) (h4/bitstring/v2n v)
%   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_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_wordss_MODu_u_2EXPu_u_DIMINDEX]: !n. h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value) = h4/bit/MOD__2EXP (h4/fcp/dimindex h4/bool/the__value) n
% 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)
% Assm [h4s_bitstrings_n2wu_u_v2n]: !v. h4/words/n2w (h4/bitstring/v2n v) = h4/bitstring/v2w v
% Goal: !v. h4/words/w2n (h4/bitstring/v2w v) = h4/bit/MOD__2EXP (h4/fcp/dimindex h4/bool/the__value) (h4/bitstring/v2n v)
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_Q89092,TV_Q89088]: ![V_f, V_g]: (![V_x]: s(TV_Q89088,happ(s(t_fun(TV_Q89092,TV_Q89088),V_f),s(TV_Q89092,V_x))) = s(TV_Q89088,happ(s(t_fun(TV_Q89092,TV_Q89088),V_g),s(TV_Q89092,V_x))) => s(t_fun(TV_Q89092,TV_Q89088),V_f) = s(t_fun(TV_Q89092,TV_Q89088),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_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
fof(ah4s_wordss_MODu_u_2EXPu_u_DIMINDEX, axiom, ![TV_u_27a]: ![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))))) = s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,V_n)))).
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(ah4s_bitstrings_n2wu_u_v2n, axiom, ![TV_u_27a]: ![V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_bitstrings_v2n(s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v)))).
fof(ch4s_bitstrings_w2nu_u_v2w, conjecture, ![TV_u_27a]: ![V_v]: s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_bitstrings_v2n(s(t_h4s_lists_list(t_bool),V_v)))))).
