%   ORIGINAL: h4/words/WORD__NEG__RMUL
% 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__MULT__COMM: !w v. h4/words/word__mul v w = h4/words/word__mul w v
% Assm: h4/words/WORD__NEG__LMUL: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul (h4/words/word__2comp v) w
% Goal: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul v (h4/words/word__2comp w)
%   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_MULTu_u_COMM]: !w v. h4/words/word__mul v w = h4/words/word__mul w v
% Assm [h4s_wordss_WORDu_u_NEGu_u_LMUL]: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul (h4/words/word__2comp v) w
% Goal: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul v (h4/words/word__2comp w)
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_Q123802,TV_Q123798]: ![V_f, V_g]: (![V_x]: s(TV_Q123798,happ(s(t_fun(TV_Q123802,TV_Q123798),V_f),s(TV_Q123802,V_x))) = s(TV_Q123798,happ(s(t_fun(TV_Q123802,TV_Q123798),V_g),s(TV_Q123802,V_x))) => s(t_fun(TV_Q123802,TV_Q123798),V_f) = s(t_fun(TV_Q123802,TV_Q123798),V_g))).
fof(ah4s_wordss_WORDu_u_MULTu_u_COMM, axiom, ![TV_u_27a]: ![V_w, V_v]: 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_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v)))).
fof(ah4s_wordss_WORDu_u_NEGu_u_LMUL, 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),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))).
fof(ch4s_wordss_WORDu_u_NEGu_u_RMUL, conjecture, ![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)))))).
