%   ORIGINAL: h4/patricia/ADD__INSERT
% 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/one/one1: !v. v = h4/one/one0
% Assm: h4/patricia/INSERT__PTREE__def: !t n. h4/patricia/INSERT__PTREE n t = h4/patricia/ADD t (h4/pair/_2C n h4/one/one0)
% Goal: !v t n. h4/patricia/ADD t (h4/pair/_2C n v) = h4/patricia/INSERT__PTREE n t
%   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_ones_one1]: !v. v = h4/one/one0
% Assm [h4s_patricias_INSERTu_u_PTREEu_u_def]: !t n. h4/patricia/INSERT__PTREE n t = h4/patricia/ADD t (h4/pair/_2C n h4/one/one0)
% Goal: !v t n. h4/patricia/ADD t (h4/pair/_2C n v) = h4/patricia/INSERT__PTREE n t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q287022,TV_Q287018]: ![V_f, V_g]: (![V_x]: s(TV_Q287018,happ(s(t_fun(TV_Q287022,TV_Q287018),V_f),s(TV_Q287022,V_x))) = s(TV_Q287018,happ(s(t_fun(TV_Q287022,TV_Q287018),V_g),s(TV_Q287022,V_x))) => s(t_fun(TV_Q287022,TV_Q287018),V_f) = s(t_fun(TV_Q287022,TV_Q287018),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_ones_one1, axiom, ![V_v]: s(t_h4s_ones_one,V_v) = s(t_h4s_ones_one,h4s_ones_one0)).
fof(ah4s_patricias_INSERTu_u_PTREEu_u_def, axiom, ![V_t, V_n]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_insertu_u_ptree(s(t_h4s_nums_num,V_n),s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_add(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_ones_one),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_ones_one,h4s_ones_one0)))))).
fof(ch4s_patricias_ADDu_u_INSERT, conjecture, ![V_v, V_t, V_n]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_add(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_ones_one),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_ones_one,V_v))))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_insertu_u_ptree(s(t_h4s_nums_num,V_n),s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t)))).
