%   ORIGINAL: h4/rat/RAT__SUB__CONG_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/rat/RAT__SUB__CONG1: !y x. h4/rat/abs__rat (h4/frac/frac__sub (h4/rat/rep__rat (h4/rat/abs__rat x)) y) = h4/rat/abs__rat (h4/frac/frac__sub x y)
% Goal: !y x. h4/rat/abs__rat (h4/frac/frac__sub (h4/rat/rep__rat (h4/rat/abs__rat x)) y) = h4/rat/abs__rat (h4/frac/frac__sub x y)
%   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_rats_RATu_u_SUBu_u_CONG1]: !y x. h4/rat/abs__rat (h4/frac/frac__sub (h4/rat/rep__rat (h4/rat/abs__rat x)) y) = h4/rat/abs__rat (h4/frac/frac__sub x y)
% Goal: !y x. h4/rat/abs__rat (h4/frac/frac__sub (h4/rat/rep__rat (h4/rat/abs__rat x)) y) = h4/rat/abs__rat (h4/frac/frac__sub x y)
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_Q91963,TV_Q91959]: ![V_f, V_g]: (![V_x]: s(TV_Q91959,happ(s(t_fun(TV_Q91963,TV_Q91959),V_f),s(TV_Q91963,V_x))) = s(TV_Q91959,happ(s(t_fun(TV_Q91963,TV_Q91959),V_g),s(TV_Q91963,V_x))) => s(t_fun(TV_Q91963,TV_Q91959),V_f) = s(t_fun(TV_Q91963,TV_Q91959),V_g))).
fof(ah4s_rats_RATu_u_SUBu_u_CONG1, axiom, ![V_y, V_x]: s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,V_x))))),s(t_h4s_fracs_frac,V_y))))) = s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,V_x),s(t_h4s_fracs_frac,V_y)))))).
fof(ch4s_rats_RATu_u_SUBu_u_CONGu_c0, conjecture, ![V_y, V_x]: s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,V_x))))),s(t_h4s_fracs_frac,V_y))))) = s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,V_x),s(t_h4s_fracs_frac,V_y)))))).
