%   ORIGINAL: 'h4/thm/list/GENLIST_EL_'
% 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: !ls f n. n = 'h4/const/list/LENGTH' ls /\ (!i. 'h4/const/prim_rec/<' i n ==> f i = 'h4/const/list/EL' i ls) ==> 'h4/const/list/GENLIST' f n = ls
%   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: !ls f n. n = 'h4/const/list/LENGTH' ls /\ (!i. 'h4/const/prim_rec/<' i n ==> happ f i = 'h4/const/list/EL' i ls) ==> 'h4/const/list/GENLIST' f n = ls
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_3f11669,V_3f11665]: ![F, G]: (![X]: s(V_3f11665,happ(s(fun(V_3f11669,V_3f11665),F),s(V_3f11669,X))) = s(V_3f11665,happ(s(fun(V_3f11669,V_3f11665),G),s(V_3f11669,X))) => s(fun(V_3f11669,V_3f11665),F) = s(fun(V_3f11669,V_3f11665),G))).
fof('h4/thm/list/GENLIST_EL_', conjecture, ![A]: ![Ls, F, N]: ((s('h4/type/num/num',N) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),Ls))) & ![I]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',I),s('h4/type/num/num',N)))) => s(A,happ(s(fun('h4/type/num/num',A),F),s('h4/type/num/num',I))) = s(A,'h4/const/list/EL'(s('h4/type/num/num',I),s('h4/type/list/list'(A),Ls))))) => s('h4/type/list/list'(A),'h4/const/list/GENLIST'(s(fun('h4/type/num/num',A),F),s('h4/type/num/num',N))) = s('h4/type/list/list'(A),Ls))).
