%   ORIGINAL: h4/bool/MONO__ALL
% 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 P. (!x. P x ==> Q x) ==> (!x. P x) ==> (!x. Q x)
%   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 P. (!x. happ P x ==> happ Q x) ==> (!x. happ P x) ==> (!x. happ Q x)
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_Q293289,TV_Q293285]: ![V_f, V_g]: (![V_x]: s(TV_Q293285,happ(s(t_fun(TV_Q293289,TV_Q293285),V_f),s(TV_Q293289,V_x))) = s(TV_Q293285,happ(s(t_fun(TV_Q293289,TV_Q293285),V_g),s(TV_Q293289,V_x))) => s(t_fun(TV_Q293289,TV_Q293285),V_f) = s(t_fun(TV_Q293289,TV_Q293285),V_g))).
fof(ch4s_bools_MONOu_u_ALL, conjecture, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
