%   ORIGINAL: h4/int__arith/le__move__all__right
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/integer/int__sub0: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/INT__ADD__LID: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm: h4/integer/INT__LE__SUB__LADD: !z y x. h4/integer/int__le x (h4/integer/int__sub y z) <=> h4/integer/int__le (h4/integer/int__add x z) y
% Goal: !y x. h4/integer/int__le x y <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add y (h4/integer/int__neg 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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_integers_intu_u_sub0]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_ADDu_u_LID]: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_LADD]: !z y x. h4/integer/int__le x (h4/integer/int__sub y z) <=> h4/integer/int__le (h4/integer/int__add x z) y
% Goal: !y x. h4/integer/int__le x y <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__add y (h4/integer/int__neg 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_Q208118,TV_Q208114]: ![V_f, V_g]: (![V_x]: s(TV_Q208114,happ(s(t_fun(TV_Q208118,TV_Q208114),V_f),s(TV_Q208118,V_x))) = s(TV_Q208114,happ(s(t_fun(TV_Q208118,TV_Q208114),V_g),s(TV_Q208118,V_x))) => s(t_fun(TV_Q208118,TV_Q208114),V_f) = s(t_fun(TV_Q208118,TV_Q208114),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_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_sub0, axiom, ![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,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_ADDu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(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,V_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(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_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_z))),s(t_h4s_integers_int,V_y)))).
fof(ch4s_intu_u_ariths_leu_u_moveu_u_allu_u_right, conjecture, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = 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_y),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))))))).
