%   ORIGINAL: h4/real/REAL__LE__MAX2
% 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/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/real/REAL__LE__REFL: !x. h4/real/real__lte x x
% Assm: h4/real/REAL__LE__MAX: !z y x. h4/real/real__lte z (h4/real/max x y) <=> h4/real/real__lte z x \/ h4/real/real__lte z y
% Goal: !y x. h4/real/real__lte y (h4/real/max 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_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_reals_REALu_u_LEu_u_REFL]: !x. h4/real/real__lte x x
% Assm [h4s_reals_REALu_u_LEu_u_MAX]: !z y x. h4/real/real__lte z (h4/real/max x y) <=> h4/real/real__lte z x \/ h4/real/real__lte z y
% Goal: !y x. h4/real/real__lte y (h4/real/max 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_Q68977,TV_Q68973]: ![V_f, V_g]: (![V_x]: s(TV_Q68973,happ(s(t_fun(TV_Q68977,TV_Q68973),V_f),s(TV_Q68977,V_x))) = s(TV_Q68973,happ(s(t_fun(TV_Q68977,TV_Q68973),V_g),s(TV_Q68977,V_x))) => s(t_fun(TV_Q68977,TV_Q68973),V_f) = s(t_fun(TV_Q68977,TV_Q68973),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_reals_REALu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_reals_REALu_u_LEu_u_MAX, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,h4s_reals_max(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))) <=> (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x)))) | p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_y))))))).
fof(ch4s_reals_REALu_u_LEu_u_MAX2, conjecture, ![V_y, V_x]: p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,h4s_reals_max(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))))).
