%   ORIGINAL: h4/words/WORD__SUB__SUB
% 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/marker/AC__DEF: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% 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__ASSOC: !x w v. h4/words/word__add v (h4/words/word__add w x) = h4/words/word__add (h4/words/word__add v w) x
% Assm: h4/words/WORD__ADD__COMM: !w v. h4/words/word__add v w = h4/words/word__add w v
% Assm: h4/words/WORD__NEG__ADD: !w v. h4/words/word__2comp (h4/words/word__add v w) = h4/words/word__add (h4/words/word__2comp v) (h4/words/word__2comp w)
% Assm: h4/words/WORD__NEG__NEG: !w. h4/words/word__2comp (h4/words/word__2comp w) = w
% Goal: !x w v. h4/words/word__sub v (h4/words/word__sub w x) = h4/words/word__sub (h4/words/word__add v x) 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_markers_ACu_u_DEF]: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% 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_ASSOC]: !x w v. h4/words/word__add v (h4/words/word__add w x) = h4/words/word__add (h4/words/word__add v w) x
% Assm [h4s_wordss_WORDu_u_ADDu_u_COMM]: !w v. h4/words/word__add v w = h4/words/word__add w v
% Assm [h4s_wordss_WORDu_u_NEGu_u_ADD]: !w v. h4/words/word__2comp (h4/words/word__add v w) = h4/words/word__add (h4/words/word__2comp v) (h4/words/word__2comp w)
% Assm [h4s_wordss_WORDu_u_NEGu_u_NEG]: !w. h4/words/word__2comp (h4/words/word__2comp w) = w
% Goal: !x w v. h4/words/word__sub v (h4/words/word__sub w x) = h4/words/word__sub (h4/words/word__add v x) 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_Q123102,TV_Q123098]: ![V_f, V_g]: (![V_x]: s(TV_Q123098,happ(s(t_fun(TV_Q123102,TV_Q123098),V_f),s(TV_Q123102,V_x))) = s(TV_Q123098,happ(s(t_fun(TV_Q123102,TV_Q123098),V_g),s(TV_Q123102,V_x))) => s(t_fun(TV_Q123102,TV_Q123098),V_f) = s(t_fun(TV_Q123102,TV_Q123098),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_markers_ACu_u_DEF, axiom, ![V_b2, V_b1]: (p(s(t_bool,h4s_markers_ac(s(t_bool,V_b1),s(t_bool,V_b2)))) <=> (p(s(t_bool,V_b1)) & p(s(t_bool,V_b2))))).
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_ASSOC, axiom, ![TV_u_27a]: ![V_x, V_w, 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_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_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))))) = 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_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),V_w))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x)))).
fof(ah4s_wordss_WORDu_u_ADDu_u_COMM, axiom, ![TV_u_27a]: ![V_w, 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_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_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v)))).
fof(ah4s_wordss_WORDu_u_NEGu_u_ADD, 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_add(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),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),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_NEGu_u_NEG, axiom, ![TV_u_27a]: ![V_w]: 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_2comp(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(ch4s_wordss_WORDu_u_SUBu_u_SUB, conjecture, ![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),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),V_x))))) = 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),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),V_x))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))).
