%   ORIGINAL: h4/frac/FRAC
% 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/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/frac/frac__bij_c0: !a. h4/frac/abs__frac (h4/frac/rep__frac a) = a
% Assm: h4/frac/frac__nmr__def: !f. h4/frac/frac__nmr f = h4/pair/FST (h4/frac/rep__frac f)
% Assm: h4/frac/frac__dnm__def: !f. h4/frac/frac__dnm f = h4/pair/SND (h4/frac/rep__frac f)
% Goal: !f. h4/frac/abs__frac (h4/pair/_2C (h4/frac/frac__nmr f) (h4/frac/frac__dnm f)) = f
%   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_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_fracs_fracu_u_biju_c0]: !a. h4/frac/abs__frac (h4/frac/rep__frac a) = a
% Assm [h4s_fracs_fracu_u_nmru_u_def]: !f. h4/frac/frac__nmr f = h4/pair/FST (h4/frac/rep__frac f)
% Assm [h4s_fracs_fracu_u_dnmu_u_def]: !f. h4/frac/frac__dnm f = h4/pair/SND (h4/frac/rep__frac f)
% Goal: !f. h4/frac/abs__frac (h4/pair/_2C (h4/frac/frac__nmr f) (h4/frac/frac__dnm f)) = f
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_Q199247,TV_Q199243]: ![V_f, V_g]: (![V_x]: s(TV_Q199243,happ(s(t_fun(TV_Q199247,TV_Q199243),V_f),s(TV_Q199247,V_x))) = s(TV_Q199243,happ(s(t_fun(TV_Q199247,TV_Q199243),V_g),s(TV_Q199247,V_x))) => s(t_fun(TV_Q199247,TV_Q199243),V_f) = s(t_fun(TV_Q199247,TV_Q199243),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_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_fracs_fracu_u_biju_c0, axiom, ![V_a]: s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,V_a))))) = s(t_h4s_fracs_frac,V_a)).
fof(ah4s_fracs_fracu_u_nmru_u_def, axiom, ![V_f]: s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,V_f))) = s(t_h4s_integers_int,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,V_f)))))).
fof(ah4s_fracs_fracu_u_dnmu_u_def, axiom, ![V_f]: s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,V_f))) = s(t_h4s_integers_int,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,V_f)))))).
fof(ch4s_fracs_FRAC, conjecture, ![V_f]: s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,V_f))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,V_f))))))) = s(t_h4s_fracs_frac,V_f)).
