%   ORIGINAL: 'h4/thm/rich_list/LASTN_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: !'longer than list' n l. 'h4/const/rich_list/LASTN' n l = 'h4/const/bool/LET' (\m. 'h4/const/bool/COND' ('h4/const/arithmetic/<=' n m) ('h4/const/list/DROP' ('h4/const/arithmetic/-' m n) l) ('h4/const/combin/FAIL' 'h4/const/rich_list/LASTN' 'longer than list' n l)) ('h4/const/list/LENGTH' 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: !_0. (!'longer than list' n l m. happ (happ (happ (happ _0 'longer than list') n) l) m = 'h4/const/bool/COND' ('h4/const/arithmetic/<=' n m) ('h4/const/list/DROP' ('h4/const/arithmetic/-' m n) l) (happ (happ ('h4/const/combin/FAIL' 'h4/const/rich_list/LASTN' 'longer than list') n) l)) ==> (!'longer than list' n l. happ (happ 'h4/const/rich_list/LASTN' n) l = 'h4/const/bool/LET' (happ (happ (happ _0 'longer than list') n) l) ('h4/const/list/LENGTH' 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_3f58686,V_3f58682]: ![F, G]: (![X]: s(V_3f58682,happ(s(fun(V_3f58686,V_3f58682),F),s(V_3f58686,X))) = s(V_3f58682,happ(s(fun(V_3f58686,V_3f58682),G),s(V_3f58686,X))) => s(fun(V_3f58686,V_3f58682),F) = s(fun(V_3f58686,V_3f58682),G))).
fof('h4/thm/rich_list/LASTN_compute_', conjecture, ![A]: ![V__0]: (![V_27longer_20than_20list_27, N, L, M]: s('h4/type/list/list'(A),happ(s(fun('h4/type/num/num','h4/type/list/list'(A)),happ(s(fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/list/list'(A))),happ(s(fun('h4/type/num/num',fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/list/list'(A)))),happ(s(fun(bool,fun('h4/type/num/num',fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/list/list'(A))))),V__0),s(bool,V_27longer_20than_20list_27))),s('h4/type/num/num',N))),s('h4/type/list/list'(A),L))),s('h4/type/num/num',M))) = s('h4/type/list/list'(A),'h4/const/bool/COND'(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',N),s('h4/type/num/num',M))),s('h4/type/list/list'(A),'h4/const/list/DROP'(s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',M),s('h4/type/num/num',N))),s('h4/type/list/list'(A),L))),s('h4/type/list/list'(A),happ(s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),happ(s(fun('h4/type/num/num',fun('h4/type/list/list'(A),'h4/type/list/list'(A))),'h4/const/combin/FAIL'(s(fun('h4/type/num/num',fun('h4/type/list/list'(A),'h4/type/list/list'(A))),'h4/const/rich_list/LASTN'),s(bool,V_27longer_20than_20list_27))),s('h4/type/num/num',N))),s('h4/type/list/list'(A),L))))) => ![V_27longer_20than_20list_27, N, L]: s('h4/type/list/list'(A),happ(s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),happ(s(fun('h4/type/num/num',fun('h4/type/list/list'(A),'h4/type/list/list'(A))),'h4/const/rich_list/LASTN'),s('h4/type/num/num',N))),s('h4/type/list/list'(A),L))) = s('h4/type/list/list'(A),'h4/const/bool/LET'(s(fun('h4/type/num/num','h4/type/list/list'(A)),happ(s(fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/list/list'(A))),happ(s(fun('h4/type/num/num',fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/list/list'(A)))),happ(s(fun(bool,fun('h4/type/num/num',fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/list/list'(A))))),V__0),s(bool,V_27longer_20than_20list_27))),s('h4/type/num/num',N))),s('h4/type/list/list'(A),L))),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L))))))).
