%   ORIGINAL: 'h4/thm/list/EL_compute_'
% 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: !l n. 'h4/const/list/EL' n l = 'h4/const/bool/COND' (n = 'h4/const/num/0') ('h4/const/list/HD' l) ('h4/const/list/EL' ('h4/const/prim_rec/PRE' n) ('h4/const/list/TL' l))
%   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: !l n. ?v. (v <=> n = 'h4/const/num/0') /\ 'h4/const/list/EL' n l = 'h4/const/bool/COND' v ('h4/const/list/HD' l) ('h4/const/list/EL' ('h4/const/prim_rec/PRE' n) ('h4/const/list/TL' l))
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_3f5238,V_3f5234]: ![F, G]: (![X]: s(V_3f5234,happ(s(fun(V_3f5238,V_3f5234),F),s(V_3f5238,X))) = s(V_3f5234,happ(s(fun(V_3f5238,V_3f5234),G),s(V_3f5238,X))) => s(fun(V_3f5238,V_3f5234),F) = s(fun(V_3f5238,V_3f5234),G))).
fof('h4/thm/list/EL_compute_', conjecture, ![A]: ![L, N]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/num/num',N) = s('h4/type/num/num','h4/const/num/0')) & s(A,'h4/const/list/EL'(s('h4/type/num/num',N),s('h4/type/list/list'(A),L))) = s(A,'h4/const/bool/COND'(s(bool,V),s(A,'h4/const/list/HD'(s('h4/type/list/list'(A),L))),s(A,'h4/const/list/EL'(s('h4/type/num/num','h4/const/prim_rec/PRE'(s('h4/type/num/num',N))),s('h4/type/list/list'(A),'h4/const/list/TL'(s('h4/type/list/list'(A),L))))))))).
