%   ORIGINAL: h4/int__arith/lt__move__left__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/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__LT__ADDNEG: !z y x. h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__neg z)) <=> h4/integer/int__lt (h4/integer/int__add y z) x
% Goal: !z y x. h4/integer/int__lt (h4/integer/int__add x y) z <=> h4/integer/int__lt y (h4/integer/int__add z (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_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_LTu_u_ADDNEG]: !z y x. h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__neg z)) <=> h4/integer/int__lt (h4/integer/int__add y z) x
% Goal: !z y x. h4/integer/int__lt (h4/integer/int__add x y) z <=> h4/integer/int__lt y (h4/integer/int__add z (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_Q208068,TV_Q208064]: ![V_f, V_g]: (![V_x]: s(TV_Q208064,happ(s(t_fun(TV_Q208068,TV_Q208064),V_f),s(TV_Q208068,V_x))) = s(TV_Q208064,happ(s(t_fun(TV_Q208068,TV_Q208064),V_g),s(TV_Q208068,V_x))) => s(t_fun(TV_Q208068,TV_Q208064),V_f) = s(t_fun(TV_Q208068,TV_Q208064),V_g))).
fof(ah4s_integers_INTu_u_ADDu_u_COMM, axiom, ![V_y, V_x]: 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_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_ADDNEG, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(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_z))))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,V_x)))).
fof(ch4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_right, conjecture, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(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,V_z))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))))))).
