%   ORIGINAL: 'h4/thm/list/SINGL_LIST_APPLY_L_'
% 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 f. 'h4/const/list/LIST_BIND' ('h4/const/list/CONS' x 'h4/const/list/NIL') f = f x
%   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 f. 'h4/const/list/LIST_BIND' ('h4/const/list/CONS' x 'h4/const/list/NIL') f = happ f x
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_3f10969,V_3f10965]: ![F, G]: (![X]: s(V_3f10965,happ(s(fun(V_3f10969,V_3f10965),F),s(V_3f10969,X))) = s(V_3f10965,happ(s(fun(V_3f10969,V_3f10965),G),s(V_3f10969,X))) => s(fun(V_3f10969,V_3f10965),F) = s(fun(V_3f10969,V_3f10965),G))).
fof('h4/thm/list/SINGL_LIST_APPLY_L_', conjecture, ![A,B]: ![X, F]: s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(B),'h4/const/list/CONS'(s(B,X),s('h4/type/list/list'(B),'h4/const/list/NIL'))),s(fun(B,'h4/type/list/list'(A)),F))) = s('h4/type/list/list'(A),happ(s(fun(B,'h4/type/list/list'(A)),F),s(B,X)))).
