%   ORIGINAL: 'h4/thm/list/datatype_list_'
% 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: !list. 'h4/const/bool/DATATYPE' (list 'h4/const/list/NIL' 'h4/const/list/CONS')
%   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: !list. 'h4/const/bool/DATATYPE' (happ (happ list 'h4/const/list/NIL') 'h4/const/list/CONS')
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_3f2388,V_3f2384]: ![F, G]: (![X]: s(V_3f2384,happ(s(fun(V_3f2388,V_3f2384),F),s(V_3f2388,X))) = s(V_3f2384,happ(s(fun(V_3f2388,V_3f2384),G),s(V_3f2388,X))) => s(fun(V_3f2388,V_3f2384),F) = s(fun(V_3f2388,V_3f2384),G))).
fof('h4/thm/list/datatype_list_', conjecture, ![A]: ![List]: p(s(bool,'h4/const/bool/DATATYPE'(s(bool,happ(s(fun(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),bool),happ(s(fun('h4/type/list/list'(A),fun(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),bool)),List),s('h4/type/list/list'(A),'h4/const/list/NIL'))),s(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),'h4/const/list/CONS'))))))).
