%   ORIGINAL: h4/rich__list/IS__PREFIX_c2
% 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__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/list/isPREFIX__THM_c2: !t2 t1 h2 h1. h4/list/isPREFIX (h4/list/CONS h1 t1) (h4/list/CONS h2 t2) <=> h1 = h2 /\ h4/list/isPREFIX t1 t2
% Goal: !x2 x1 l2 l1. h4/list/isPREFIX (h4/list/CONS x2 l2) (h4/list/CONS x1 l1) <=> x1 = x2 /\ h4/list/isPREFIX l2 l1
%   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_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_lists_isPREFIXu_u_THMu_c2]: !t2 t1 h2 h1. h4/list/isPREFIX (h4/list/CONS h1 t1) (h4/list/CONS h2 t2) <=> h1 = h2 /\ h4/list/isPREFIX t1 t2
% Goal: !x2 x1 l2 l1. h4/list/isPREFIX (h4/list/CONS x2 l2) (h4/list/CONS x1 l1) <=> x1 = x2 /\ h4/list/isPREFIX l2 l1
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_Q158958,TV_Q158954]: ![V_f, V_g]: (![V_x]: s(TV_Q158954,happ(s(t_fun(TV_Q158958,TV_Q158954),V_f),s(TV_Q158958,V_x))) = s(TV_Q158954,happ(s(t_fun(TV_Q158958,TV_Q158954),V_g),s(TV_Q158958,V_x))) => s(t_fun(TV_Q158958,TV_Q158954),V_f) = s(t_fun(TV_Q158958,TV_Q158954),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_lists_isPREFIXu_u_THMu_c2, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_h2, V_h1]: (p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h1),s(t_h4s_lists_list(TV_u_27a),V_t1))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h2),s(t_h4s_lists_list(TV_u_27a),V_t2)))))) <=> (s(TV_u_27a,V_h1) = s(TV_u_27a,V_h2) & p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),V_t1),s(t_h4s_lists_list(TV_u_27a),V_t2))))))).
fof(ch4s_richu_u_lists_ISu_u_PREFIXu_c2, conjecture, ![TV_u_27a]: ![V_x2, V_x1, V_l2, V_l1]: (p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x2),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x1),s(t_h4s_lists_list(TV_u_27a),V_l1)))))) <=> (s(TV_u_27a,V_x1) = s(TV_u_27a,V_x2) & p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l1))))))).
