%   ORIGINAL: h4/real/REAL__NEG__LE0
% 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__lte0: !y x. h4/real/real__lte x y <=> ~h4/realax/real__lt y x
% Assm: h4/real/REAL__NEG__GT0: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__neg x) <=> h4/realax/real__lt x (h4/real/real__of__num h4/num/0)
% Goal: !x. h4/real/real__lte (h4/realax/real__neg x) (h4/real/real__of__num h4/num/0) <=> h4/real/real__lte (h4/real/real__of__num h4/num/0) 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_lte0]: !y x. h4/real/real__lte x y <=> ~h4/realax/real__lt y x
% Assm [h4s_reals_REALu_u_NEGu_u_GT0]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__neg x) <=> h4/realax/real__lt x (h4/real/real__of__num h4/num/0)
% Goal: !x. h4/real/real__lte (h4/realax/real__neg x) (h4/real/real__of__num h4/num/0) <=> h4/real/real__lte (h4/real/real__of__num h4/num/0) 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_Q61526,TV_Q61522]: ![V_f, V_g]: (![V_x]: s(TV_Q61522,happ(s(t_fun(TV_Q61526,TV_Q61522),V_f),s(TV_Q61526,V_x))) = s(TV_Q61522,happ(s(t_fun(TV_Q61526,TV_Q61522),V_g),s(TV_Q61526,V_x))) => s(t_fun(TV_Q61526,TV_Q61522),V_f) = s(t_fun(TV_Q61526,TV_Q61522),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_lte0, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) <=> ~ (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_NEGu_u_GT0, axiom, ![V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ch4s_reals_REALu_u_NEGu_u_LE0, conjecture, ![V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))).
