%   ORIGINAL: 'h4/thm/list/splitAtPki_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: !l1 l2 P k. 'h4/const/list/EVERYi' (\i. 'h4/const/combin/o' $not (P i)) l1 /\ ('h4/const/prim_rec/<' 'h4/const/num/0' ('h4/const/list/LENGTH' l2) ==> P ('h4/const/list/LENGTH' l1) ('h4/const/list/HD' l2)) ==> 'h4/const/list/splitAtPki' P k ('h4/const/list/APPEND' l1 l2) = k l1 l2
%   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. (!P i. happ (happ _0 P) i = 'h4/const/combin/o' $not (happ P i)) ==> (!l1 l2 P k. 'h4/const/list/EVERYi' (happ _0 P) l1 /\ ('h4/const/prim_rec/<' 'h4/const/num/0' ('h4/const/list/LENGTH' l2) ==> happ (happ P ('h4/const/list/LENGTH' l1)) ('h4/const/list/HD' l2)) ==> 'h4/const/list/splitAtPki' P k ('h4/const/list/APPEND' l1 l2) = happ (happ k l1) l2)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f10619,V_3f10615]: ![F, G]: (![X]: s(V_3f10615,happ(s(fun(V_3f10619,V_3f10615),F),s(V_3f10619,X))) = s(V_3f10615,happ(s(fun(V_3f10619,V_3f10615),G),s(V_3f10619,X))) => s(fun(V_3f10619,V_3f10615),F) = s(fun(V_3f10619,V_3f10615),G))).
fof('h4/thm/list/splitAtPki_APPEND_', conjecture, ![B,A]: ![V__0]: (![P, I]: s(fun(A,bool),happ(s(fun('h4/type/num/num',fun(A,bool)),happ(s(fun(fun('h4/type/num/num',fun(A,bool)),fun('h4/type/num/num',fun(A,bool))),V__0),s(fun('h4/type/num/num',fun(A,bool)),P))),s('h4/type/num/num',I))) = s(fun(A,bool),'h4/const/combin/o'(s(fun(bool,bool),'$not'),s(fun(A,bool),happ(s(fun('h4/type/num/num',fun(A,bool)),P),s('h4/type/num/num',I))))) => ![L1, L2, P, K]: ((p(s(bool,'h4/const/list/EVERYi'(s(fun('h4/type/num/num',fun(A,bool)),happ(s(fun(fun('h4/type/num/num',fun(A,bool)),fun('h4/type/num/num',fun(A,bool))),V__0),s(fun('h4/type/num/num',fun(A,bool)),P))),s('h4/type/list/list'(A),L1)))) & (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L2)))))) => p(s(bool,happ(s(fun(A,bool),happ(s(fun('h4/type/num/num',fun(A,bool)),P),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))))),s(A,'h4/const/list/HD'(s('h4/type/list/list'(A),L2)))))))) => s(B,'h4/const/list/splitAtPki'(s(fun('h4/type/num/num',fun(A,bool)),P),s(fun('h4/type/list/list'(A),fun('h4/type/list/list'(A),B)),K),s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L2))))) = s(B,happ(s(fun('h4/type/list/list'(A),B),happ(s(fun('h4/type/list/list'(A),fun('h4/type/list/list'(A),B)),K),s('h4/type/list/list'(A),L1))),s('h4/type/list/list'(A),L2)))))).
