%   ORIGINAL: h4/int__arith/eq__context__rwt1
% 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/integer/INT__LE__LADD: !z y x. h4/integer/int__le (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__le y z
% Goal: !y x c. h4/integer/int__of__num h4/num/0 = h4/integer/int__add c x ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add c y) <=> h4/integer/int__le 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_integers_INTu_u_LEu_u_LADD]: !z y x. h4/integer/int__le (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__le y z
% Goal: !y x c. h4/integer/int__of__num h4/num/0 = h4/integer/int__add c x ==> (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add c y) <=> h4/integer/int__le 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_Q209626,TV_Q209622]: ![V_f, V_g]: (![V_x]: s(TV_Q209622,happ(s(t_fun(TV_Q209626,TV_Q209622),V_f),s(TV_Q209626,V_x))) = s(TV_Q209622,happ(s(t_fun(TV_Q209626,TV_Q209622),V_g),s(TV_Q209626,V_x))) => s(t_fun(TV_Q209626,TV_Q209622),V_f) = s(t_fun(TV_Q209626,TV_Q209622),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_integers_INTu_u_LEu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),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_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))).
fof(ch4s_intu_u_ariths_equ_u_contextu_u_rwt1, conjecture, ![V_y, V_x, V_c]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_x))) => s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_y))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))).
