%   ORIGINAL: h4/integer/INT__EQ__SUB__RADD
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/integer/INT__EQ__SUB__LADD: !z y x. x = h4/integer/int__sub y z <=> h4/integer/int__add x z = y
% Goal: !z y x. h4/integer/int__sub x y = z <=> x = h4/integer/int__add z 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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_integers_INTu_u_EQu_u_SUBu_u_LADD]: !z y x. x = h4/integer/int__sub y z <=> h4/integer/int__add x z = y
% Goal: !z y x. h4/integer/int__sub x y = z <=> x = h4/integer/int__add z 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_Q4775,TV_Q4771]: ![V_f, V_g]: (![V_x]: s(TV_Q4771,happ(s(t_fun(TV_Q4775,TV_Q4771),V_f),s(TV_Q4775,V_x))) = s(TV_Q4771,happ(s(t_fun(TV_Q4775,TV_Q4771),V_g),s(TV_Q4775,V_x))) => s(t_fun(TV_Q4775,TV_Q4771),V_f) = s(t_fun(TV_Q4775,TV_Q4771),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_integers_INTu_u_EQu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))) <=> s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))) = s(t_h4s_integers_int,V_y))).
fof(ch4s_integers_INTu_u_EQu_u_SUBu_u_RADD, conjecture, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,V_z) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y))))).
