%   ORIGINAL: h4/rat/RAT__SUB__CONG1
% 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/frac/frac__sub__def: !f2 f1. h4/frac/frac__sub f1 f2 = h4/frac/frac__add f1 (h4/frac/frac__ainv f2)
% Assm: h4/rat/RAT__ADD__CONG_c0: !y x. h4/rat/abs__rat (h4/frac/frac__add (h4/rat/rep__rat (h4/rat/abs__rat x)) y) = h4/rat/abs__rat (h4/frac/frac__add 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_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_fracs_fracu_u_subu_u_def]: !f2 f1. h4/frac/frac__sub f1 f2 = h4/frac/frac__add f1 (h4/frac/frac__ainv f2)
% Assm [h4s_rats_RATu_u_ADDu_u_CONGu_c0]: !y x. h4/rat/abs__rat (h4/frac/frac__add (h4/rat/rep__rat (h4/rat/abs__rat x)) y) = h4/rat/abs__rat (h4/frac/frac__add 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_Q91913,TV_Q91909]: ![V_f, V_g]: (![V_x]: s(TV_Q91909,happ(s(t_fun(TV_Q91913,TV_Q91909),V_f),s(TV_Q91913,V_x))) = s(TV_Q91909,happ(s(t_fun(TV_Q91913,TV_Q91909),V_g),s(TV_Q91913,V_x))) => s(t_fun(TV_Q91913,TV_Q91909),V_f) = s(t_fun(TV_Q91913,TV_Q91909),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_fracs_fracu_u_subu_u_def, axiom, ![V_f2, V_f1]: s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,V_f1),s(t_h4s_fracs_frac,V_f2))) = s(t_h4s_fracs_frac,h4s_fracs_fracu_u_add(s(t_h4s_fracs_frac,V_f1),s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,V_f2)))))).
fof(ah4s_rats_RATu_u_ADDu_u_CONGu_c0, axiom, ![V_y, V_x]: s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_add(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_add(s(t_h4s_fracs_frac,V_x),s(t_h4s_fracs_frac,V_y)))))).
fof(ch4s_rats_RATu_u_SUBu_u_CONG1, 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)))))).
