%   ORIGINAL: 'h4/thm/pred_set/count_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/pred_set/count' ('h4/const/arithmetic/+' n m) = 'h4/const/pred_set/UNION' ('h4/const/pred_set/count' n) ('h4/const/pred_set/IMAGE' ('h4/const/arithmetic/+' n) ('h4/const/pred_set/count' 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: !n m. 'h4/const/pred_set/count' (happ ('h4/const/arithmetic/+' n) m) = 'h4/const/pred_set/UNION' ('h4/const/pred_set/count' n) ('h4/const/pred_set/IMAGE' ('h4/const/arithmetic/+' n) ('h4/const/pred_set/count' 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_3f25403,V_3f25399]: ![F, G]: (![X]: s(V_3f25399,happ(s(fun(V_3f25403,V_3f25399),F),s(V_3f25403,X))) = s(V_3f25399,happ(s(fun(V_3f25403,V_3f25399),G),s(V_3f25403,X))) => s(fun(V_3f25403,V_3f25399),F) = s(fun(V_3f25403,V_3f25399),G))).
fof('h4/thm/pred_set/count_add_', conjecture, ![N, M]: s(fun('h4/type/num/num',bool),'h4/const/pred_set/count'(s('h4/type/num/num',happ(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/+'(s('h4/type/num/num',N))),s('h4/type/num/num',M))))) = s(fun('h4/type/num/num',bool),'h4/const/pred_set/UNION'(s(fun('h4/type/num/num',bool),'h4/const/pred_set/count'(s('h4/type/num/num',N))),s(fun('h4/type/num/num',bool),'h4/const/pred_set/IMAGE'(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/+'(s('h4/type/num/num',N))),s(fun('h4/type/num/num',bool),'h4/const/pred_set/count'(s('h4/type/num/num',M)))))))).
