%   ORIGINAL: 'h4/thm/list/MEM_DROP_'
% 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 ls n. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/DROP' n ls)) <=> 'h4/const/prim_rec/<' n ('h4/const/list/LENGTH' ls) /\ x = 'h4/const/list/EL' n ls \/ 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/DROP' ('h4/const/num/SUC' 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: !x ls n. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/DROP' n ls)) <=> 'h4/const/prim_rec/<' n ('h4/const/list/LENGTH' ls) /\ x = 'h4/const/list/EL' n ls \/ 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/DROP' ('h4/const/num/SUC' 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_3f7290,V_3f7286]: ![F, G]: (![X]: s(V_3f7286,happ(s(fun(V_3f7290,V_3f7286),F),s(V_3f7290,X))) = s(V_3f7286,happ(s(fun(V_3f7290,V_3f7286),G),s(V_3f7290,X))) => s(fun(V_3f7290,V_3f7286),F) = s(fun(V_3f7290,V_3f7286),G))).
fof('h4/thm/list/MEM_DROP_', conjecture, ![A]: ![X, Ls, N]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),'h4/const/list/DROP'(s('h4/type/num/num',N),s('h4/type/list/list'(A),Ls)))))))) <=> ((p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),Ls)))))) & s(A,X) = s(A,'h4/const/list/EL'(s('h4/type/num/num',N),s('h4/type/list/list'(A),Ls)))) | p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),'h4/const/list/DROP'(s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))),s('h4/type/list/list'(A),Ls))))))))))).
