%   ORIGINAL: h4/hreal/HRAT__LT__ADD2
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/hrat/HRAT__ADD__SYM: !i h. h4/hrat/hrat__add h i = h4/hrat/hrat__add i h
% Assm: h4/hrat/HRAT__ADD__ASSOC: !j i h. h4/hrat/hrat__add h (h4/hrat/hrat__add i j) = h4/hrat/hrat__add (h4/hrat/hrat__add h i) j
% Assm: h4/hreal/hrat__lt0: !y x. h4/hreal/hrat__lt x y <=> (?d. y = h4/hrat/hrat__add x d)
% Goal: !y x v u. h4/hreal/hrat__lt u x /\ h4/hreal/hrat__lt v y ==> h4/hreal/hrat__lt (h4/hrat/hrat__add u v) (h4/hrat/hrat__add 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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_hrats_HRATu_u_ADDu_u_SYM]: !i h. h4/hrat/hrat__add h i = h4/hrat/hrat__add i h
% Assm [h4s_hrats_HRATu_u_ADDu_u_ASSOC]: !j i h. h4/hrat/hrat__add h (h4/hrat/hrat__add i j) = h4/hrat/hrat__add (h4/hrat/hrat__add h i) j
% Assm [h4s_hreals_hratu_u_lt0]: !y x. h4/hreal/hrat__lt x y <=> (?d. y = h4/hrat/hrat__add x d)
% Goal: !y x v u. h4/hreal/hrat__lt u x /\ h4/hreal/hrat__lt v y ==> h4/hreal/hrat__lt (h4/hrat/hrat__add u v) (h4/hrat/hrat__add 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_Q253931,TV_Q253927]: ![V_f, V_g]: (![V_x]: s(TV_Q253927,happ(s(t_fun(TV_Q253931,TV_Q253927),V_f),s(TV_Q253931,V_x))) = s(TV_Q253927,happ(s(t_fun(TV_Q253931,TV_Q253927),V_g),s(TV_Q253931,V_x))) => s(t_fun(TV_Q253931,TV_Q253927),V_f) = s(t_fun(TV_Q253931,TV_Q253927),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_hrats_HRATu_u_ADDu_u_SYM, axiom, ![V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_h)))).
fof(ah4s_hrats_HRATu_u_ADDu_u_ASSOC, axiom, ![V_j, V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_j))))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))),s(t_h4s_hrats_hrat,V_j)))).
fof(ah4s_hreals_hratu_u_lt0, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))) <=> ?[V_d]: s(t_h4s_hrats_hrat,V_y) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_d))))).
fof(ch4s_hreals_HRATu_u_LTu_u_ADD2, conjecture, ![V_y, V_x, V_v, V_u]: ((p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_u),s(t_h4s_hrats_hrat,V_x)))) & p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_v),s(t_h4s_hrats_hrat,V_y))))) => p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_u),s(t_h4s_hrats_hrat,V_v))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))))))).
