%   ORIGINAL: h4/words/WORD__SUB__RZERO
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/words/word__sub__def: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% Assm: h4/words/WORD__ADD__0_c0: !w. h4/words/word__add w (h4/words/n2w h4/num/0) = w
% Assm: h4/words/WORD__NEG__0: h4/words/word__2comp (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Goal: !w. h4/words/word__sub w (h4/words/n2w h4/num/0) = 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_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_wordss_wordu_u_subu_u_def]: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% Assm [h4s_wordss_WORDu_u_ADDu_u_0u_c0]: !w. h4/words/word__add w (h4/words/n2w h4/num/0) = w
% Assm [h4s_wordss_WORDu_u_NEGu_u_0]: h4/words/word__2comp (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Goal: !w. h4/words/word__sub w (h4/words/n2w h4/num/0) = 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_Q123327,TV_Q123323]: ![V_f, V_g]: (![V_x]: s(TV_Q123323,happ(s(t_fun(TV_Q123327,TV_Q123323),V_f),s(TV_Q123327,V_x))) = s(TV_Q123323,happ(s(t_fun(TV_Q123327,TV_Q123323),V_g),s(TV_Q123327,V_x))) => s(t_fun(TV_Q123327,TV_Q123323),V_f) = s(t_fun(TV_Q123327,TV_Q123323),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_subu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(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_add(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_ADDu_u_0u_c0, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)).
fof(ah4s_wordss_WORDu_u_NEGu_u_0, axiom, ![TV_u_27a]: 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_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_wordss_WORDu_u_SUBu_u_RZERO, conjecture, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)).
