%   ORIGINAL: h4/rich__list/IS__PREFIX_c1
% 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/list/isPREFIX__THM_c1: !t h. h4/list/isPREFIX (h4/list/CONS h t) h4/list/NIL <=> F
% Goal: !x l. h4/list/isPREFIX (h4/list/CONS x l) h4/list/NIL <=> F
%   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_lists_isPREFIXu_u_THMu_c1]: !t h. h4/list/isPREFIX (h4/list/CONS h t) h4/list/NIL <=> F
% Goal: !x l. h4/list/isPREFIX (h4/list/CONS x l) h4/list/NIL <=> F
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_Q158933,TV_Q158929]: ![V_f, V_g]: (![V_x]: s(TV_Q158929,happ(s(t_fun(TV_Q158933,TV_Q158929),V_f),s(TV_Q158933,V_x))) = s(TV_Q158929,happ(s(t_fun(TV_Q158933,TV_Q158929),V_g),s(TV_Q158933,V_x))) => s(t_fun(TV_Q158933,TV_Q158929),V_f) = s(t_fun(TV_Q158933,TV_Q158929),V_g))).
fof(ah4s_lists_isPREFIXu_u_THMu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,f)).
fof(ch4s_richu_u_lists_ISu_u_PREFIXu_c1, conjecture, ![TV_u_27a]: ![V_x, V_l]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,f)).
