%   ORIGINAL: h4/quotient/CONJ__IMPLIES
% 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
% Goal: !Q_27 Q P_27 P. (P ==> Q) /\ (P_27 ==> Q_27) ==> P /\ P_27 ==> Q /\ Q_27
%   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
% Goal: !Q_27 Q P_27 P. (P ==> Q) /\ (P_27 ==> Q_27) ==> P /\ P_27 ==> Q /\ Q_27
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_Q226108,TV_Q226104]: ![V_f, V_g]: (![V_x]: s(TV_Q226104,happ(s(t_fun(TV_Q226108,TV_Q226104),V_f),s(TV_Q226108,V_x))) = s(TV_Q226104,happ(s(t_fun(TV_Q226108,TV_Q226104),V_g),s(TV_Q226108,V_x))) => s(t_fun(TV_Q226108,TV_Q226104),V_f) = s(t_fun(TV_Q226108,TV_Q226104),V_g))).
fof(ch4s_quotients_CONJu_u_IMPLIES, conjecture, ![V_Qu_27, V_Q, V_Pu_27, V_P]: (((p(s(t_bool,V_P)) => p(s(t_bool,V_Q))) & (p(s(t_bool,V_Pu_27)) => p(s(t_bool,V_Qu_27)))) => ((p(s(t_bool,V_P)) & p(s(t_bool,V_Pu_27))) => (p(s(t_bool,V_Q)) & p(s(t_bool,V_Qu_27)))))).
