%   ORIGINAL: h4/sptree/insert__compute_c0
% 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/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Goal: !t n a. h4/sptree/insert (h4/arithmetic/NUMERAL n) a t = h4/sptree/insert n a 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_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Goal: !t n a. h4/sptree/insert (h4/arithmetic/NUMERAL n) a t = h4/sptree/insert n a 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_Q83395,TV_Q83391]: ![V_f, V_g]: (![V_x]: s(TV_Q83391,happ(s(t_fun(TV_Q83395,TV_Q83391),V_f),s(TV_Q83395,V_x))) = s(TV_Q83391,happ(s(t_fun(TV_Q83395,TV_Q83391),V_g),s(TV_Q83395,V_x))) => s(t_fun(TV_Q83395,TV_Q83391),V_f) = s(t_fun(TV_Q83395,TV_Q83391),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_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ch4s_sptrees_insertu_u_computeu_c0, conjecture, ![TV_u_27a]: ![V_t, V_n, V_a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_insert(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_a),s(t_h4s_sptrees_spt(TV_u_27a),V_t))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_insert(s(t_h4s_nums_num,V_n),s(TV_u_27a,V_a),s(t_h4s_sptrees_spt(TV_u_27a),V_t)))).
