%   ORIGINAL: 'h4/thm/rich_list/count_list_sub1_'
% 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. ~(n = 'h4/const/num/0') ==> 'h4/const/rich_list/COUNT_LIST' n = 'h4/const/list/CONS' 'h4/const/num/0' ('h4/const/list/MAP' 'h4/const/num/SUC' ('h4/const/rich_list/COUNT_LIST' ('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. ~(n = 'h4/const/num/0') ==> 'h4/const/rich_list/COUNT_LIST' n = 'h4/const/list/CONS' 'h4/const/num/0' ('h4/const/list/MAP' 'h4/const/num/SUC' ('h4/const/rich_list/COUNT_LIST' ('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_3f58261,V_3f58257]: ![F, G]: (![X]: s(V_3f58257,happ(s(fun(V_3f58261,V_3f58257),F),s(V_3f58261,X))) = s(V_3f58257,happ(s(fun(V_3f58261,V_3f58257),G),s(V_3f58261,X))) => s(fun(V_3f58261,V_3f58257),F) = s(fun(V_3f58261,V_3f58257),G))).
fof('h4/thm/rich_list/count_list_sub1_', conjecture, ![N]: (~ (s('h4/type/num/num',N) = s('h4/type/num/num','h4/const/num/0')) => 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/CONS'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/MAP'(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/num/SUC'),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','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))))))))))).
