%   ORIGINAL: 'h4/thm/list/LIST_BIND_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: !l2 l1 f. 'h4/const/list/LIST_BIND' ('h4/const/list/APPEND' l1 l2) f = 'h4/const/list/APPEND' ('h4/const/list/LIST_BIND' l1 f) ('h4/const/list/LIST_BIND' l2 f)
%   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: !l2 l1 f. 'h4/const/list/LIST_BIND' ('h4/const/list/APPEND' l1 l2) f = 'h4/const/list/APPEND' ('h4/const/list/LIST_BIND' l1 f) ('h4/const/list/LIST_BIND' l2 f)
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_3f10869,V_3f10865]: ![F, G]: (![X]: s(V_3f10865,happ(s(fun(V_3f10869,V_3f10865),F),s(V_3f10869,X))) = s(V_3f10865,happ(s(fun(V_3f10869,V_3f10865),G),s(V_3f10869,X))) => s(fun(V_3f10869,V_3f10865),F) = s(fun(V_3f10869,V_3f10865),G))).
fof('h4/thm/list/LIST_BIND_APPEND_', conjecture, ![B,A]: ![L2, L1, F]: s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(B),'h4/const/list/APPEND'(s('h4/type/list/list'(B),L1),s('h4/type/list/list'(B),L2))),s(fun(B,'h4/type/list/list'(A)),F))) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(B),L1),s(fun(B,'h4/type/list/list'(A)),F))),s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(B),L2),s(fun(B,'h4/type/list/list'(A)),F)))))).
