%   ORIGINAL: h4/words/WORD__EQ__SUB__ZERO
% 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__ADD__0_c1: !w. h4/words/word__add (h4/words/n2w h4/num/0) w = w
% Assm: h4/words/WORD__EQ__SUB__RADD: !x w v. h4/words/word__sub v w = x <=> v = h4/words/word__add x w
% Goal: !w v. h4/words/word__sub v w = h4/words/n2w h4/num/0 <=> v = 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_ADDu_u_0u_c1]: !w. h4/words/word__add (h4/words/n2w h4/num/0) w = w
% Assm [h4s_wordss_WORDu_u_EQu_u_SUBu_u_RADD]: !x w v. h4/words/word__sub v w = x <=> v = h4/words/word__add x w
% Goal: !w v. h4/words/word__sub v w = h4/words/n2w h4/num/0 <=> v = 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_Q123202,TV_Q123198]: ![V_f, V_g]: (![V_x]: s(TV_Q123198,happ(s(t_fun(TV_Q123202,TV_Q123198),V_f),s(TV_Q123202,V_x))) = s(TV_Q123198,happ(s(t_fun(TV_Q123202,TV_Q123198),V_g),s(TV_Q123202,V_x))) => s(t_fun(TV_Q123202,TV_Q123198),V_f) = s(t_fun(TV_Q123202,TV_Q123198),V_g))).
fof(ah4s_wordss_WORDu_u_ADDu_u_0u_c1, 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),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)).
fof(ah4s_wordss_WORDu_u_EQu_u_SUBu_u_RADD, axiom, ![TV_u_27a]: ![V_x, 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),V_x) <=> 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_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))).
fof(ch4s_wordss_WORDu_u_EQu_u_SUBu_u_ZERO, conjecture, ![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_n2w(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))).
