%   ORIGINAL: h4/patricia__casts/ADD__INSERT__WORD
% 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/one/one__axiom: !g f. f = g
% Goal: !w v t. h4/patricia__casts/ADDw t (h4/pair/_2C w v) = h4/patricia__casts/ADDw t (h4/pair/_2C w h4/one/one0)
%   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_ones_oneu_u_axiom]: !g f. f = g
% Goal: !w v t. h4/patricia__casts/ADDw t (h4/pair/_2C w v) = h4/patricia__casts/ADDw t (h4/pair/_2C w h4/one/one0)
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_Q205122,TV_Q205118]: ![V_f, V_g]: (![V_x]: s(TV_Q205118,happ(s(t_fun(TV_Q205122,TV_Q205118),V_f),s(TV_Q205122,V_x))) = s(TV_Q205118,happ(s(t_fun(TV_Q205122,TV_Q205118),V_g),s(TV_Q205122,V_x))) => s(t_fun(TV_Q205122,TV_Q205118),V_f) = s(t_fun(TV_Q205122,TV_Q205118),V_g))).
fof(ah4s_ones_oneu_u_axiom, axiom, ![TV_u_27a]: ![V_g, V_f]: s(t_fun(TV_u_27a,t_h4s_ones_one),V_f) = s(t_fun(TV_u_27a,t_h4s_ones_one),V_g)).
fof(ch4s_patriciau_u_castss_ADDu_u_INSERTu_u_WORD, conjecture, ![TV_u_27a]: ![V_w, V_v, V_t]: s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,t_h4s_ones_one),h4s_patriciau_u_castss_addw(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,t_h4s_ones_one),V_t),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_ones_one),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_ones_one,V_v))))) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,t_h4s_ones_one),h4s_patriciau_u_castss_addw(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,t_h4s_ones_one),V_t),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_ones_one),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_ones_one,h4s_ones_one0)))))).
