%   ORIGINAL: 'h4/thm/list/dropWhile_splitAtPki_'
% 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: !P. 'h4/const/list/dropWhile' P = 'h4/const/list/splitAtPki' ('h4/const/combin/C' ('h4/const/combin/o' 'h4/const/combin/K' ('h4/const/combin/o' $not P))) ('h4/const/combin/K' 'h4/const/combin/I')
%   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: !P. 'h4/const/list/dropWhile' P = 'h4/const/list/splitAtPki' ('h4/const/combin/C' ('h4/const/combin/o' 'h4/const/combin/K' ('h4/const/combin/o' $not P))) (happ 'h4/const/combin/K' 'h4/const/combin/I')
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f12669,V_3f12665]: ![F, G]: (![X]: s(V_3f12665,happ(s(fun(V_3f12669,V_3f12665),F),s(V_3f12669,X))) = s(V_3f12665,happ(s(fun(V_3f12669,V_3f12665),G),s(V_3f12669,X))) => s(fun(V_3f12669,V_3f12665),F) = s(fun(V_3f12669,V_3f12665),G))).
fof('h4/thm/list/dropWhile_splitAtPki_', conjecture, ![A]: ![P]: s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),'h4/const/list/dropWhile'(s(fun(A,bool),P))) = s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),'h4/const/list/splitAtPki'(s(fun('h4/type/num/num',fun(A,bool)),'h4/const/combin/C'(s(fun(A,fun('h4/type/num/num',bool)),'h4/const/combin/o'(s(fun(bool,fun('h4/type/num/num',bool)),'h4/const/combin/K'),s(fun(A,bool),'h4/const/combin/o'(s(fun(bool,bool),'$not'),s(fun(A,bool),P))))))),s(fun('h4/type/list/list'(A),fun('h4/type/list/list'(A),'h4/type/list/list'(A))),happ(s(fun(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),fun('h4/type/list/list'(A),fun('h4/type/list/list'(A),'h4/type/list/list'(A)))),'h4/const/combin/K'),s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),'h4/const/combin/I')))))).
