%   ORIGINAL: h4/hreal/HRAT__LT__RMUL1
% 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/hrat/HRAT__MUL__SYM: !i h. h4/hrat/hrat__mul h i = h4/hrat/hrat__mul i h
% Assm: h4/hreal/HRAT__LT__LMUL1: !y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul x y) y <=> h4/hreal/hrat__lt x h4/hrat/hrat__1
% Goal: !y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul x y) x <=> h4/hreal/hrat__lt y h4/hrat/hrat__1
%   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_hrats_HRATu_u_MULu_u_SYM]: !i h. h4/hrat/hrat__mul h i = h4/hrat/hrat__mul i h
% Assm [h4s_hreals_HRATu_u_LTu_u_LMUL1]: !y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul x y) y <=> h4/hreal/hrat__lt x h4/hrat/hrat__1
% Goal: !y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul x y) x <=> h4/hreal/hrat__lt y h4/hrat/hrat__1
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_Q254106,TV_Q254102]: ![V_f, V_g]: (![V_x]: s(TV_Q254102,happ(s(t_fun(TV_Q254106,TV_Q254102),V_f),s(TV_Q254106,V_x))) = s(TV_Q254102,happ(s(t_fun(TV_Q254106,TV_Q254102),V_g),s(TV_Q254106,V_x))) => s(t_fun(TV_Q254106,TV_Q254102),V_f) = s(t_fun(TV_Q254106,TV_Q254102),V_g))).
fof(ah4s_hrats_HRATu_u_MULu_u_SYM, axiom, ![V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_h)))).
fof(ah4s_hreals_HRATu_u_LTu_u_LMUL1, axiom, ![V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y))),s(t_h4s_hrats_hrat,V_y))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)))).
fof(ch4s_hreals_HRATu_u_LTu_u_RMUL1, conjecture, ![V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y))),s(t_h4s_hrats_hrat,V_x))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_y),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)))).
