%   ORIGINAL: h4/words/word__eq__n2w_c0
% 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/bit/MOD__2EXP__EQ__def: !n b a. h4/bit/MOD__2EXP__EQ n a b <=> h4/bit/MOD__2EXP n a = h4/bit/MOD__2EXP n b
% 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/n2w__11: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Goal: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/bit/MOD__2EXP__EQ (h4/fcp/dimindex h4/bool/the__value) m n
%   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_bits_MODu_u_2EXPu_u_EQu_u_def]: !n b a. h4/bit/MOD__2EXP__EQ n a b <=> h4/bit/MOD__2EXP n a = h4/bit/MOD__2EXP n b
% 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_n2wu_u_11]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Goal: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/bit/MOD__2EXP__EQ (h4/fcp/dimindex h4/bool/the__value) m n
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_Q128700,TV_Q128696]: ![V_f, V_g]: (![V_x]: s(TV_Q128696,happ(s(t_fun(TV_Q128700,TV_Q128696),V_f),s(TV_Q128700,V_x))) = s(TV_Q128696,happ(s(t_fun(TV_Q128700,TV_Q128696),V_g),s(TV_Q128700,V_x))) => s(t_fun(TV_Q128700,TV_Q128696),V_f) = s(t_fun(TV_Q128700,TV_Q128696),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_bits_MODu_u_2EXPu_u_EQu_u_def, axiom, ![V_n, V_b, V_a]: (p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b)))) <=> s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))) = s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_b))))).
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_n2wu_u_11, axiom, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = 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_m),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_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_wordu_u_equ_u_n2wu_c0, conjecture, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) <=> p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(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_m),s(t_h4s_nums_num,V_n)))))).
