%   ORIGINAL: h4/real/REAL__ADD__SUB__ALT
% 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/real/REAL__EQ__SUB__RADD: !z y x. h4/real/real__sub x y = z <=> x = h4/realax/real__add z y
% Goal: !y x. h4/real/real__sub (h4/realax/real__add x y) y = 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_reals_REALu_u_EQu_u_SUBu_u_RADD]: !z y x. h4/real/real__sub x y = z <=> x = h4/realax/real__add z y
% Goal: !y x. h4/real/real__sub (h4/realax/real__add x y) y = 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_Q70264,TV_Q70260]: ![V_f, V_g]: (![V_x]: s(TV_Q70260,happ(s(t_fun(TV_Q70264,TV_Q70260),V_f),s(TV_Q70264,V_x))) = s(TV_Q70260,happ(s(t_fun(TV_Q70264,TV_Q70260),V_g),s(TV_Q70264,V_x))) => s(t_fun(TV_Q70264,TV_Q70260),V_f) = s(t_fun(TV_Q70264,TV_Q70260),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_reals_REALu_u_EQu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: (s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,V_z) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_y))))).
fof(ch4s_reals_REALu_u_ADDu_u_SUBu_u_ALT, conjecture, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,V_x)).
