%   ORIGINAL: h4/arithmetic/num__case__cong
% 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/arithmetic/num__case__def_c0: !v f. h4/arithmetic/num__CASE h4/num/0 v f = v
% Assm: h4/arithmetic/num__case__def_c1: !v n f. h4/arithmetic/num__CASE (h4/num/SUC n) v f = f n
% Assm: h4/arithmetic/num__CASES: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Goal: !v_27 v f_27 f M_27 M. M = M_27 /\ (M_27 = h4/num/0 ==> v = v_27) /\ (!n. M_27 = h4/num/SUC n ==> f n = f_27 n) ==> h4/arithmetic/num__CASE M v f = h4/arithmetic/num__CASE M_27 v_27 f_27
%   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_arithmetics_numu_u_caseu_u_defu_c0]: !v f. h4/arithmetic/num__CASE h4/num/0 v f = v
% Assm [h4s_arithmetics_numu_u_caseu_u_defu_c1]: !v n f. h4/arithmetic/num__CASE (h4/num/SUC n) v f = happ f n
% Assm [h4s_arithmetics_numu_u_CASES]: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Goal: !v_27 v f_27 f M_27 M. M = M_27 /\ (M_27 = h4/num/0 ==> v = v_27) /\ (!n. M_27 = h4/num/SUC n ==> happ f n = happ f_27 n) ==> h4/arithmetic/num__CASE M v f = h4/arithmetic/num__CASE M_27 v_27 f_27
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q311198,TV_Q311194]: ![V_f, V_g]: (![V_x]: s(TV_Q311194,happ(s(t_fun(TV_Q311198,TV_Q311194),V_f),s(TV_Q311198,V_x))) = s(TV_Q311194,happ(s(t_fun(TV_Q311198,TV_Q311194),V_g),s(TV_Q311198,V_x))) => s(t_fun(TV_Q311198,TV_Q311194),V_f) = s(t_fun(TV_Q311198,TV_Q311194),V_g))).
fof(ah4s_arithmetics_numu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v, V_f]: s(TV_u_27a,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_v),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))) = s(TV_u_27a,V_v)).
fof(ah4s_arithmetics_numu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v, V_n, V_f]: s(TV_u_27a,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_v),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_numu_u_CASES, axiom, ![V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0) | ?[V_n]: s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))).
fof(ch4s_arithmetics_numu_u_caseu_u_cong, conjecture, ![TV_u_27a]: ![V_vu_27, V_v, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_nums_num,V_M) = s(t_h4s_nums_num,V_Mu_27) & ((s(t_h4s_nums_num,V_Mu_27) = s(t_h4s_nums_num,h4s_nums_0) => s(TV_u_27a,V_v) = s(TV_u_27a,V_vu_27)) & ![V_n]: (s(t_h4s_nums_num,V_Mu_27) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) => s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_fu_27),s(t_h4s_nums_num,V_n)))))) => s(TV_u_27a,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,V_M),s(TV_u_27a,V_v),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))) = s(TV_u_27a,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,V_Mu_27),s(TV_u_27a,V_vu_27),s(t_fun(t_h4s_nums_num,TV_u_27a),V_fu_27))))).
