%   ORIGINAL: 'h4/thm/rich_list/COUNT_LIST_ADD_'
% 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 m. 'h4/const/rich_list/COUNT_LIST' ('h4/const/arithmetic/+' n m) = 'h4/const/list/APPEND' ('h4/const/rich_list/COUNT_LIST' n) ('h4/const/list/MAP' (\'n\''. 'h4/const/arithmetic/+' 'n\'' n) ('h4/const/rich_list/COUNT_LIST' m))
%   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. (!n 'n\''. happ (happ _0 n) 'n\'' = 'h4/const/arithmetic/+' 'n\'' n) ==> (!n m. 'h4/const/rich_list/COUNT_LIST' ('h4/const/arithmetic/+' n m) = 'h4/const/list/APPEND' ('h4/const/rich_list/COUNT_LIST' n) ('h4/const/list/MAP' (happ _0 n) ('h4/const/rich_list/COUNT_LIST' m)))
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_3f57136,V_3f57132]: ![F, G]: (![X]: s(V_3f57132,happ(s(fun(V_3f57136,V_3f57132),F),s(V_3f57136,X))) = s(V_3f57132,happ(s(fun(V_3f57136,V_3f57132),G),s(V_3f57136,X))) => s(fun(V_3f57136,V_3f57132),F) = s(fun(V_3f57136,V_3f57132),G))).
fof('h4/thm/rich_list/COUNT_LIST_ADD_', conjecture, ![V__0]: (![N, V_27n_5c_27_27]: s('h4/type/num/num',happ(s(fun('h4/type/num/num','h4/type/num/num'),happ(s(fun('h4/type/num/num',fun('h4/type/num/num','h4/type/num/num')),V__0),s('h4/type/num/num',N))),s('h4/type/num/num',V_27n_5c_27_27))) = s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',V_27n_5c_27_27),s('h4/type/num/num',N))) => ![N, M]: s('h4/type/list/list'('h4/type/num/num'),'h4/const/rich_list/COUNT_LIST'(s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',N),s('h4/type/num/num',M))))) = s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/APPEND'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/rich_list/COUNT_LIST'(s('h4/type/num/num',N))),s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/MAP'(s(fun('h4/type/num/num','h4/type/num/num'),happ(s(fun('h4/type/num/num',fun('h4/type/num/num','h4/type/num/num')),V__0),s('h4/type/num/num',N))),s('h4/type/list/list'('h4/type/num/num'),'h4/const/rich_list/COUNT_LIST'(s('h4/type/num/num',M))))))))).
