%   ORIGINAL: h4/combin/FAIL__THM
% 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/combin/FAIL__DEF: h4/combin/FAIL = (\x y. x)
% Goal: !y x. h4/combin/FAIL x y = 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
% Assm [h4s_combins_FAILu_u_DEF]: !x x. h4/combin/FAIL x x = x
% Goal: !y x. h4/combin/FAIL x y = 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_Q222305,TV_Q222301]: ![V_f, V_g]: (![V_x]: s(TV_Q222301,happ(s(t_fun(TV_Q222305,TV_Q222301),V_f),s(TV_Q222305,V_x))) = s(TV_Q222301,happ(s(t_fun(TV_Q222305,TV_Q222301),V_g),s(TV_Q222305,V_x))) => s(t_fun(TV_Q222305,TV_Q222301),V_f) = s(t_fun(TV_Q222305,TV_Q222301),V_g))).
fof(ah4s_combins_FAILu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27a,h4s_combins_fail(s(TV_u_27a,V_x),s(TV_u_27b,V_x0))) = s(TV_u_27a,V_x)).
fof(ch4s_combins_FAILu_u_THM, conjecture, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_combins_fail(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
