%   ORIGINAL: 'h4/thm/list/DISJOINT_GENLIST_PLUS_'
% 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: !x n b a. 'h4/const/pred_set/DISJOINT' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/GENLIST' ('h4/const/arithmetic/+' n) ('h4/const/arithmetic/+' a b))) ==> 'h4/const/pred_set/DISJOINT' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/GENLIST' ('h4/const/arithmetic/+' n) a)) /\ 'h4/const/pred_set/DISJOINT' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/GENLIST' ('h4/const/arithmetic/+' ('h4/const/arithmetic/+' n a)) b))
%   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: !x n b a. 'h4/const/pred_set/DISJOINT' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/GENLIST' ('h4/const/arithmetic/+' n) (happ ('h4/const/arithmetic/+' a) b))) ==> 'h4/const/pred_set/DISJOINT' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/GENLIST' ('h4/const/arithmetic/+' n) a)) /\ 'h4/const/pred_set/DISJOINT' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/GENLIST' ('h4/const/arithmetic/+' (happ ('h4/const/arithmetic/+' n) a)) b))
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_3f12344,V_3f12340]: ![F, G]: (![X]: s(V_3f12340,happ(s(fun(V_3f12344,V_3f12340),F),s(V_3f12344,X))) = s(V_3f12340,happ(s(fun(V_3f12344,V_3f12340),G),s(V_3f12344,X))) => s(fun(V_3f12344,V_3f12340),F) = s(fun(V_3f12344,V_3f12340),G))).
fof('h4/thm/list/DISJOINT_GENLIST_PLUS_', conjecture, ![X, N, B, A]: (p(s(bool,'h4/const/pred_set/DISJOINT'(s(fun('h4/type/num/num',bool),X),s(fun('h4/type/num/num',bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/GENLIST'(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/+'(s('h4/type/num/num',N))),s('h4/type/num/num',happ(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/+'(s('h4/type/num/num',A))),s('h4/type/num/num',B)))))))))) => (p(s(bool,'h4/const/pred_set/DISJOINT'(s(fun('h4/type/num/num',bool),X),s(fun('h4/type/num/num',bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/GENLIST'(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/+'(s('h4/type/num/num',N))),s('h4/type/num/num',A)))))))) & p(s(bool,'h4/const/pred_set/DISJOINT'(s(fun('h4/type/num/num',bool),X),s(fun('h4/type/num/num',bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/GENLIST'(s(fun('h4/type/num/num','h4/type/num/num'),'h4/const/arithmetic/+'(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',A))))),s('h4/type/num/num',B))))))))))).
