%   ORIGINAL: 'h4/thm/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
% Goal: !b N M. 'h4/const/bool/literal_case' (\x. N x) M b = 'h4/const/bool/literal_case' (\x. N x b) M
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% 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/const/bool/literal_case' (happ _0 N) M) b = 'h4/const/bool/literal_case' (happ (happ _1 N) b) M))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f35428,V_3f35424]: ![F, G]: (![X]: s(V_3f35424,happ(s(fun(V_3f35428,V_3f35424),F),s(V_3f35428,X))) = s(V_3f35424,happ(s(fun(V_3f35428,V_3f35424),G),s(V_3f35428,X))) => s(fun(V_3f35428,V_3f35424),F) = s(fun(V_3f35428,V_3f35424),G))).
fof('h4/thm/bool/literal_case_RATOR_', conjecture, ![C,B,A]: ![V__1]: (![N, B0, X]: s(C,happ(s(fun(A,C),happ(s(fun(B,fun(A,C)),happ(s(fun(fun(A,fun(B,C)),fun(B,fun(A,C))),V__1),s(fun(A,fun(B,C)),N))),s(B,B0))),s(A,X))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),N),s(A,X))),s(B,B0))) => ![V__0]: (![N, X]: s(fun(B,C),happ(s(fun(A,fun(B,C)),happ(s(fun(fun(A,fun(B,C)),fun(A,fun(B,C))),V__0),s(fun(A,fun(B,C)),N))),s(A,X))) = s(fun(B,C),happ(s(fun(A,fun(B,C)),N),s(A,X))) => ![B0, N, M]: s(C,happ(s(fun(B,C),'h4/const/bool/literal_case'(s(fun(A,fun(B,C)),happ(s(fun(fun(A,fun(B,C)),fun(A,fun(B,C))),V__0),s(fun(A,fun(B,C)),N))),s(A,M))),s(B,B0))) = s(C,'h4/const/bool/literal_case'(s(fun(A,C),happ(s(fun(B,fun(A,C)),happ(s(fun(fun(A,fun(B,C)),fun(B,fun(A,C))),V__1),s(fun(A,fun(B,C)),N))),s(B,B0))),s(A,M)))))).
