%   ORIGINAL: 'h4/thm/bool/literal_case_id_'
% 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: !u t a. 'h4/const/bool/literal_case' (\x. 'h4/const/bool/COND' (x = a) t u) a = t
%   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: !_0. (!a t u x. ?v. (v <=> x = a) /\ happ (happ (happ (happ _0 a) t) u) x = 'h4/const/bool/COND' v t u) ==> (!u t a. 'h4/const/bool/literal_case' (happ (happ (happ _0 a) t) u) a = t)
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_3f35478,V_3f35474]: ![F, G]: (![X]: s(V_3f35474,happ(s(fun(V_3f35478,V_3f35474),F),s(V_3f35478,X))) = s(V_3f35474,happ(s(fun(V_3f35478,V_3f35474),G),s(V_3f35478,X))) => s(fun(V_3f35478,V_3f35474),F) = s(fun(V_3f35478,V_3f35474),G))).
fof('h4/thm/bool/literal_case_id_', conjecture, ![A,B]: ![V__0]: (![A0, T, U, X]: ?[V]: ((p(s(bool,V)) <=> s(A,X) = s(A,A0)) & s(B,happ(s(fun(A,B),happ(s(fun(B,fun(A,B)),happ(s(fun(B,fun(B,fun(A,B))),happ(s(fun(A,fun(B,fun(B,fun(A,B)))),V__0),s(A,A0))),s(B,T))),s(B,U))),s(A,X))) = s(B,'h4/const/bool/COND'(s(bool,V),s(B,T),s(B,U)))) => ![U, T, A0]: s(B,'h4/const/bool/literal_case'(s(fun(A,B),happ(s(fun(B,fun(A,B)),happ(s(fun(B,fun(B,fun(A,B))),happ(s(fun(A,fun(B,fun(B,fun(A,B)))),V__0),s(A,A0))),s(B,T))),s(B,U))),s(A,A0))) = s(B,T))).
