%   ORIGINAL: 'h4/thm/list/SINGL_LIST_APPLY_R_'
% 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: !l. 'h4/const/list/LIST_BIND' l (\x. 'h4/const/list/CONS' x 'h4/const/list/NIL') = l
%   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. (!x. happ _0 x = 'h4/const/list/CONS' x 'h4/const/list/NIL') ==> (!l. 'h4/const/list/LIST_BIND' l _0 = l)
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_3f10994,V_3f10990]: ![F, G]: (![X]: s(V_3f10990,happ(s(fun(V_3f10994,V_3f10990),F),s(V_3f10994,X))) = s(V_3f10990,happ(s(fun(V_3f10994,V_3f10990),G),s(V_3f10994,X))) => s(fun(V_3f10994,V_3f10990),F) = s(fun(V_3f10994,V_3f10990),G))).
fof('h4/thm/list/SINGL_LIST_APPLY_R_', conjecture, ![A]: ![V__0]: (![X]: s('h4/type/list/list'(A),happ(s(fun(A,'h4/type/list/list'(A)),V__0),s(A,X))) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X),s('h4/type/list/list'(A),'h4/const/list/NIL'))) => ![L]: s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(A),L),s(fun(A,'h4/type/list/list'(A)),V__0))) = s('h4/type/list/list'(A),L))).
