%   ORIGINAL: h4/sptree/delete__compute_c1
% 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/sptree/delete__def_c0: !k. h4/sptree/delete k h4/sptree/LN = h4/sptree/LN
% Goal: h4/sptree/delete h4/num/0 h4/sptree/LN = h4/sptree/LN
%   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_sptrees_deleteu_u_defu_c0]: !k. h4/sptree/delete k h4/sptree/LN = h4/sptree/LN
% Goal: h4/sptree/delete h4/num/0 h4/sptree/LN = h4/sptree/LN
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_Q83909,TV_Q83905]: ![V_f, V_g]: (![V_x]: s(TV_Q83905,happ(s(t_fun(TV_Q83909,TV_Q83905),V_f),s(TV_Q83909,V_x))) = s(TV_Q83905,happ(s(t_fun(TV_Q83909,TV_Q83905),V_g),s(TV_Q83909,V_x))) => s(t_fun(TV_Q83909,TV_Q83905),V_f) = s(t_fun(TV_Q83909,TV_Q83905),V_g))).
fof(ah4s_sptrees_deleteu_u_defu_c0, axiom, ![TV_u_27a]: ![V_k]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_delete(s(t_h4s_nums_num,V_k),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln)).
fof(ch4s_sptrees_deleteu_u_computeu_c1, conjecture, ![TV_u_27a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_delete(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln)).
