%   ORIGINAL: h4/rich__list/IS__PREFIX__APPEND3
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/rich__list/APPEND__NIL_c0: !l. h4/list/APPEND l h4/list/NIL = l
% Assm: h4/rich__list/IS__PREFIX_c0: !l. h4/list/isPREFIX h4/list/NIL l <=> T
% Assm: h4/rich__list/IS__PREFIX__APPENDS: !c b a. h4/list/isPREFIX (h4/list/APPEND a b) (h4/list/APPEND a c) <=> h4/list/isPREFIX b c
% Goal: !c a. h4/list/isPREFIX a (h4/list/APPEND a c)
%   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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_richu_u_lists_APPENDu_u_NILu_c0]: !l. h4/list/APPEND l h4/list/NIL = l
% Assm [h4s_richu_u_lists_ISu_u_PREFIXu_c0]: !l. h4/list/isPREFIX h4/list/NIL l <=> T
% Assm [h4s_richu_u_lists_ISu_u_PREFIXu_u_APPENDS]: !c b a. h4/list/isPREFIX (h4/list/APPEND a b) (h4/list/APPEND a c) <=> h4/list/isPREFIX b c
% Goal: !c a. h4/list/isPREFIX a (h4/list/APPEND a c)
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_Q163985,TV_Q163981]: ![V_f, V_g]: (![V_x]: s(TV_Q163981,happ(s(t_fun(TV_Q163985,TV_Q163981),V_f),s(TV_Q163985,V_x))) = s(TV_Q163981,happ(s(t_fun(TV_Q163985,TV_Q163981),V_g),s(TV_Q163985,V_x))) => s(t_fun(TV_Q163985,TV_Q163981),V_f) = s(t_fun(TV_Q163985,TV_Q163981),V_g))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_richu_u_lists_APPENDu_u_NILu_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_richu_u_lists_ISu_u_PREFIXu_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,t)).
fof(ah4s_richu_u_lists_ISu_u_PREFIXu_u_APPENDS, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_a),s(t_h4s_lists_list(TV_u_27a),V_b))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_a),s(t_h4s_lists_list(TV_u_27a),V_c))))) = s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),V_b),s(t_h4s_lists_list(TV_u_27a),V_c)))).
fof(ch4s_richu_u_lists_ISu_u_PREFIXu_u_APPEND3, conjecture, ![TV_u_27a]: ![V_c, V_a]: p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),V_a),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_a),s(t_h4s_lists_list(TV_u_27a),V_c))))))).
