%   ORIGINAL: 'h4/thm/ind_type/FCONS_DEST_'
% 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: !n f a. 'h4/const/ind_type/FCONS' a f n = 'h4/const/bool/COND' (n = 'h4/const/num/0') a (f ('h4/const/arithmetic/-' n ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))))
%   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: !n f a. ?v. (v <=> n = 'h4/const/num/0') /\ 'h4/const/ind_type/FCONS' a f n = 'h4/const/bool/COND' v a (happ f ('h4/const/arithmetic/-' n ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))))
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_3f74289,V_3f74285]: ![F, G]: (![X]: s(V_3f74285,happ(s(fun(V_3f74289,V_3f74285),F),s(V_3f74289,X))) = s(V_3f74285,happ(s(fun(V_3f74289,V_3f74285),G),s(V_3f74289,X))) => s(fun(V_3f74289,V_3f74285),F) = s(fun(V_3f74289,V_3f74285),G))).
fof('h4/thm/ind_type/FCONS_DEST_', conjecture, ![A]: ![N, F, A0]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/num/num',N) = s('h4/type/num/num','h4/const/num/0')) & s(A,'h4/const/ind_type/FCONS'(s(A,A0),s(fun('h4/type/num/num',A),F),s('h4/type/num/num',N))) = s(A,'h4/const/bool/COND'(s(bool,V),s(A,A0),s(A,happ(s(fun('h4/type/num/num',A),F),s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))))))))).
