%   ORIGINAL: 'h4/thm/list/LAST_CONS_cond_'
% 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: !t h. 'h4/const/list/LAST' ('h4/const/list/CONS' h t) = 'h4/const/bool/COND' (t = 'h4/const/list/NIL') h ('h4/const/list/LAST' 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: !t h. ?v. (v <=> t = 'h4/const/list/NIL') /\ 'h4/const/list/LAST' ('h4/const/list/CONS' h t) = 'h4/const/bool/COND' v h ('h4/const/list/LAST' 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_3f7039,V_3f7035]: ![F, G]: (![X]: s(V_3f7035,happ(s(fun(V_3f7039,V_3f7035),F),s(V_3f7039,X))) = s(V_3f7035,happ(s(fun(V_3f7039,V_3f7035),G),s(V_3f7039,X))) => s(fun(V_3f7039,V_3f7035),F) = s(fun(V_3f7039,V_3f7035),G))).
fof('h4/thm/list/LAST_CONS_cond_', conjecture, ![A]: ![T, H]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/list/list'(A),T) = s('h4/type/list/list'(A),'h4/const/list/NIL')) & s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),T))))) = s(A,'h4/const/bool/COND'(s(bool,V),s(A,H),s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),T))))))).
