%   ORIGINAL: h4/hrat/TRAT__EQ__AP
% 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/TRAT__EQ__REFL: !p. h4/hrat/trat__eq p p
% Goal: !q p. p = q ==> h4/hrat/trat__eq p q
%   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_TRATu_u_EQu_u_REFL]: !p. h4/hrat/trat__eq p p
% Goal: !q p. p = q ==> h4/hrat/trat__eq p q
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_Q86603,TV_Q86599]: ![V_f, V_g]: (![V_x]: s(TV_Q86599,happ(s(t_fun(TV_Q86603,TV_Q86599),V_f),s(TV_Q86603,V_x))) = s(TV_Q86599,happ(s(t_fun(TV_Q86603,TV_Q86599),V_g),s(TV_Q86603,V_x))) => s(t_fun(TV_Q86603,TV_Q86599),V_f) = s(t_fun(TV_Q86603,TV_Q86599),V_g))).
fof(ah4s_hrats_TRATu_u_EQu_u_REFL, axiom, ![V_p]: p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_p),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_p))))).
fof(ch4s_hrats_TRATu_u_EQu_u_AP, conjecture, ![V_q, V_p]: (s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_p) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_q) => p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_p),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_q)))))).
