%   ORIGINAL: h4/relation/EqIsBothRSUBSET
% 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/relation/WeakOrder__EQ: !R. h4/relation/WeakOrder R ==> (!y z. y = z <=> R y z /\ R z y)
% Assm: h4/relation/RSUBSET__WeakOrder: h4/relation/WeakOrder h4/relation/RSUBSET
% Goal: !z y. y = z <=> h4/relation/RSUBSET y z /\ h4/relation/RSUBSET z 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_relations_WeakOrderu_u_EQ]: !R. h4/relation/WeakOrder R ==> (!y z. y = z <=> happ (happ R y) z /\ happ (happ R z) y)
% Assm [h4s_relations_RSUBSETu_u_WeakOrder]: h4/relation/WeakOrder h4/relation/RSUBSET
% Goal: !z y. y = z <=> happ (happ h4/relation/RSUBSET y) z /\ happ (happ h4/relation/RSUBSET z) 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_Q265482,TV_Q265478]: ![V_f, V_g]: (![V_x]: s(TV_Q265478,happ(s(t_fun(TV_Q265482,TV_Q265478),V_f),s(TV_Q265482,V_x))) = s(TV_Q265478,happ(s(t_fun(TV_Q265482,TV_Q265478),V_g),s(TV_Q265482,V_x))) => s(t_fun(TV_Q265482,TV_Q265478),V_f) = s(t_fun(TV_Q265482,TV_Q265478),V_g))).
fof(ah4s_relations_WeakOrderu_u_EQ, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_weakorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_y, V_z]: (s(TV_u_27a,V_y) = s(TV_u_27a,V_z) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y)))))))).
fof(ah4s_relations_RSUBSETu_u_WeakOrder, axiom, ![TV_u_27a,TV_u_27b]: p(s(t_bool,h4s_relations_weakorder(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool)),h4s_relations_rsubset))))).
fof(ch4s_relations_EqIsBothRSUBSET, conjecture, ![TV_u_27a,TV_u_27b]: ![V_z, V_y]: (s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_y) = s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_z) <=> (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool)),h4s_relations_rsubset),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_y))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_z)))) & p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool)),h4s_relations_rsubset),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_z))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_y))))))).
