%   ORIGINAL: h4/bool/literal__case__RATOR
% 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/bool/literal__case__DEF: h4/bool/literal__case = (\f x. f x)
% Goal: !b N M. h4/bool/literal__case (\x. N x) M b = h4/bool/literal__case (\x. N x b) M
%   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_bools_literalu_u_caseu_u_DEF]: !x x. h4/bool/literal__case x x = happ x x
% Goal: !_1. (!N b x. happ (happ (happ _1 N) b) x = happ (happ N x) b) ==> (!_0. (!N x. happ (happ _0 N) x = happ N x) ==> (!b N M. happ (h4/bool/literal__case (happ _0 N) M) b = h4/bool/literal__case (happ (happ _1 N) b) M))
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_Q294014,TV_Q294010]: ![V_f, V_g]: (![V_x]: s(TV_Q294010,happ(s(t_fun(TV_Q294014,TV_Q294010),V_f),s(TV_Q294014,V_x))) = s(TV_Q294010,happ(s(t_fun(TV_Q294014,TV_Q294010),V_g),s(TV_Q294014,V_x))) => s(t_fun(TV_Q294014,TV_Q294010),V_f) = s(t_fun(TV_Q294014,TV_Q294010),V_g))).
fof(ah4s_bools_literalu_u_caseu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_literalu_u_case(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
fof(ch4s_bools_literalu_u_caseu_u_RATOR, conjecture, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_uu_1]: (![V_N, V_b, V_x]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27c))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_N))),s(TV_u_27b,V_b))),s(TV_u_27a,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_N),s(TV_u_27a,V_x))),s(TV_u_27b,V_b))) => ![V_uu_0]: (![V_N, V_x]: s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_N))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_N),s(TV_u_27a,V_x))) => ![V_b, V_N, V_M]: s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),h4s_bools_literalu_u_case(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_N))),s(TV_u_27a,V_M))),s(TV_u_27b,V_b))) = s(TV_u_27c,h4s_bools_literalu_u_case(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27c))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_N))),s(TV_u_27b,V_b))),s(TV_u_27a,V_M)))))).
