%   ORIGINAL: h4/patricia__casts/THE__PTREE__SOME__PTREE
% 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/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/patricia__casts/THE__PTREE__def: !t a. h4/patricia__casts/THE__PTREE (h4/patricia__casts/Word__ptree a t) = t
% Assm: h4/patricia__casts/SOME__PTREE__def: !t. h4/patricia__casts/SOME__PTREE t = h4/patricia__casts/Word__ptree (h4/combin/K h4/one/one0) t
% Goal: !t. h4/patricia__casts/THE__PTREE (h4/patricia__casts/SOME__PTREE t) = 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_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_patriciau_u_castss_THEu_u_PTREEu_u_def]: !t a. h4/patricia__casts/THE__PTREE (h4/patricia__casts/Word__ptree a t) = t
% Assm [h4s_patriciau_u_castss_SOMEu_u_PTREEu_u_def]: !t. h4/patricia__casts/SOME__PTREE t = h4/patricia__casts/Word__ptree (h4/combin/K h4/one/one0) t
% Goal: !t. h4/patricia__casts/THE__PTREE (h4/patricia__casts/SOME__PTREE t) = 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_Q205147,TV_Q205143]: ![V_f, V_g]: (![V_x]: s(TV_Q205143,happ(s(t_fun(TV_Q205147,TV_Q205143),V_f),s(TV_Q205147,V_x))) = s(TV_Q205143,happ(s(t_fun(TV_Q205147,TV_Q205143),V_g),s(TV_Q205147,V_x))) => s(t_fun(TV_Q205147,TV_Q205143),V_f) = s(t_fun(TV_Q205147,TV_Q205143),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t0)))).
fof(ah4s_patriciau_u_castss_THEu_u_PTREEu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_a]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patriciau_u_castss_theu_u_ptree(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27b,TV_u_27a),h4s_patriciau_u_castss_wordu_u_ptree(s(t_fun(TV_u_27b,t_h4s_ones_one),V_a),s(t_h4s_patricias_ptree(TV_u_27a),V_t))))) = s(t_h4s_patricias_ptree(TV_u_27a),V_t)).
fof(ah4s_patriciau_u_castss_SOMEu_u_PTREEu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_t]: s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),h4s_patriciau_u_castss_someu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27b),V_t))) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),h4s_patriciau_u_castss_wordu_u_ptree(s(t_fun(TV_u_27a,t_h4s_ones_one),h4s_combins_k(s(t_h4s_ones_one,h4s_ones_one0))),s(t_h4s_patricias_ptree(TV_u_27b),V_t)))).
fof(ch4s_patriciau_u_castss_THEu_u_PTREEu_u_SOMEu_u_PTREE, conjecture, ![TV_u_27b,TV_u_27a]: ![V_t]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patriciau_u_castss_theu_u_ptree(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27b,TV_u_27a),h4s_patriciau_u_castss_someu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),V_t))))) = s(t_h4s_patricias_ptree(TV_u_27a),V_t)).
