%   ORIGINAL: h4/words/WORD__2COMP__LSL
% 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/words/WORD__NEG__RMUL: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul v (h4/words/word__2comp w)
% Assm: h4/words/WORD__MUL__LSL: !n a. h4/words/word__lsl a n = h4/words/word__mul (h4/words/n2w (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)) a
% Goal: !n a. h4/words/word__lsl (h4/words/word__2comp a) n = h4/words/word__2comp (h4/words/word__lsl a 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_wordss_WORDu_u_NEGu_u_RMUL]: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul v (h4/words/word__2comp w)
% Assm [h4s_wordss_WORDu_u_MULu_u_LSL]: !n a. h4/words/word__lsl a n = h4/words/word__mul (h4/words/n2w (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)) a
% Goal: !n a. h4/words/word__lsl (h4/words/word__2comp a) n = h4/words/word__2comp (h4/words/word__lsl a 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_Q125734,TV_Q125730]: ![V_f, V_g]: (![V_x]: s(TV_Q125730,happ(s(t_fun(TV_Q125734,TV_Q125730),V_f),s(TV_Q125734,V_x))) = s(TV_Q125730,happ(s(t_fun(TV_Q125734,TV_Q125730),V_g),s(TV_Q125734,V_x))) => s(t_fun(TV_Q125734,TV_Q125730),V_f) = s(t_fun(TV_Q125734,TV_Q125730),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_wordss_WORDu_u_NEGu_u_RMUL, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_MULu_u_LSL, axiom, ![TV_u_27a]: ![V_n, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ch4s_wordss_WORDu_u_2COMPu_u_LSL, conjecture, ![TV_u_27a]: ![V_n, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_nums_num,V_n)))))).
