%   ORIGINAL: h4/pred__set/pair__to__num__inv_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/numpair/npair0: !n. h4/numpair/npair (h4/numpair/nfst n) (h4/numpair/nsnd n) = n
% Assm: h4/pred__set/num__to__pair__def: !n. h4/pred__set/num__to__pair n = h4/pair/_2C (h4/numpair/nfst n) (h4/numpair/nsnd n)
% Assm: h4/pred__set/pair__to__num__def: !n m. h4/pred__set/pair__to__num (h4/pair/_2C m n) = h4/numpair/npair m n
% Goal: !x. h4/pred__set/pair__to__num (h4/pred__set/num__to__pair x) = x
%   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_numpairs_npair0]: !n. h4/numpair/npair (h4/numpair/nfst n) (h4/numpair/nsnd n) = n
% Assm [h4s_predu_u_sets_numu_u_tou_u_pairu_u_def]: !n. h4/pred__set/num__to__pair n = h4/pair/_2C (h4/numpair/nfst n) (h4/numpair/nsnd n)
% Assm [h4s_predu_u_sets_pairu_u_tou_u_numu_u_def]: !n m. h4/pred__set/pair__to__num (h4/pair/_2C m n) = h4/numpair/npair m n
% Goal: !x. h4/pred__set/pair__to__num (h4/pred__set/num__to__pair x) = x
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_Q156502,TV_Q156498]: ![V_f, V_g]: (![V_x]: s(TV_Q156498,happ(s(t_fun(TV_Q156502,TV_Q156498),V_f),s(TV_Q156502,V_x))) = s(TV_Q156498,happ(s(t_fun(TV_Q156502,TV_Q156498),V_g),s(TV_Q156502,V_x))) => s(t_fun(TV_Q156502,TV_Q156498),V_f) = s(t_fun(TV_Q156502,TV_Q156498),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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,t)))).
fof(ah4s_numpairs_npair0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,h4s_numpairs_nfst(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_predu_u_sets_numu_u_tou_u_pairu_u_def, axiom, ![V_n]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_predu_u_sets_numu_u_tou_u_pair(s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_numpairs_nfst(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_predu_u_sets_pairu_u_tou_u_numu_u_def, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_predu_u_sets_pairu_u_tou_u_num(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ch4s_predu_u_sets_pairu_u_tou_u_numu_u_invu_c0, conjecture, ![V_x]: s(t_h4s_nums_num,h4s_predu_u_sets_pairu_u_tou_u_num(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_predu_u_sets_numu_u_tou_u_pair(s(t_h4s_nums_num,V_x))))) = s(t_h4s_nums_num,V_x)).
