%   ORIGINAL: 'h4/thm/list/GENLIST_APPEND_'
% 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: !f a b. 'h4/const/list/GENLIST' f ('h4/const/arithmetic/+' a b) = 'h4/const/list/APPEND' ('h4/const/list/GENLIST' f b) ('h4/const/list/GENLIST' (\t. f ('h4/const/arithmetic/+' t b)) a)
%   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. (!f b t. happ (happ (happ _0 f) b) t = happ f ('h4/const/arithmetic/+' t b)) ==> (!f a b. 'h4/const/list/GENLIST' f ('h4/const/arithmetic/+' a b) = 'h4/const/list/APPEND' ('h4/const/list/GENLIST' f b) ('h4/const/list/GENLIST' (happ (happ _0 f) b) a))
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_3f9341,V_3f9337]: ![F, G]: (![X]: s(V_3f9337,happ(s(fun(V_3f9341,V_3f9337),F),s(V_3f9341,X))) = s(V_3f9337,happ(s(fun(V_3f9341,V_3f9337),G),s(V_3f9341,X))) => s(fun(V_3f9341,V_3f9337),F) = s(fun(V_3f9341,V_3f9337),G))).
fof('h4/thm/list/GENLIST_APPEND_', conjecture, ![A]: ![V__0]: (![F, B, T]: s(A,happ(s(fun('h4/type/num/num',A),happ(s(fun('h4/type/num/num',fun('h4/type/num/num',A)),happ(s(fun(fun('h4/type/num/num',A),fun('h4/type/num/num',fun('h4/type/num/num',A))),V__0),s(fun('h4/type/num/num',A),F))),s('h4/type/num/num',B))),s('h4/type/num/num',T))) = s(A,happ(s(fun('h4/type/num/num',A),F),s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',T),s('h4/type/num/num',B))))) => ![F, A0, B]: s('h4/type/list/list'(A),'h4/const/list/GENLIST'(s(fun('h4/type/num/num',A),F),s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',A0),s('h4/type/num/num',B))))) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/GENLIST'(s(fun('h4/type/num/num',A),F),s('h4/type/num/num',B))),s('h4/type/list/list'(A),'h4/const/list/GENLIST'(s(fun('h4/type/num/num',A),happ(s(fun('h4/type/num/num',fun('h4/type/num/num',A)),happ(s(fun(fun('h4/type/num/num',A),fun('h4/type/num/num',fun('h4/type/num/num',A))),V__0),s(fun('h4/type/num/num',A),F))),s('h4/type/num/num',B))),s('h4/type/num/num',A0))))))).
