%   ORIGINAL: 'h4/thm/list/LIST_BIND_MAP_'
% 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 g f. 'h4/const/list/LIST_BIND' ('h4/const/list/MAP' f l) g = 'h4/const/list/LIST_BIND' l ('h4/const/combin/o' g 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: !l g f. 'h4/const/list/LIST_BIND' ('h4/const/list/MAP' f l) g = 'h4/const/list/LIST_BIND' l ('h4/const/combin/o' g 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_3f10894,V_3f10890]: ![F, G]: (![X]: s(V_3f10890,happ(s(fun(V_3f10894,V_3f10890),F),s(V_3f10894,X))) = s(V_3f10890,happ(s(fun(V_3f10894,V_3f10890),G),s(V_3f10894,X))) => s(fun(V_3f10894,V_3f10890),F) = s(fun(V_3f10894,V_3f10890),G))).
fof('h4/thm/list/LIST_BIND_MAP_', conjecture, ![A,C,B]: ![L, G, F]: s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(C,B),F),s('h4/type/list/list'(C),L))),s(fun(B,'h4/type/list/list'(A)),G))) = s('h4/type/list/list'(A),'h4/const/list/LIST_BIND'(s('h4/type/list/list'(C),L),s(fun(C,'h4/type/list/list'(A)),'h4/const/combin/o'(s(fun(B,'h4/type/list/list'(A)),G),s(fun(C,B),F)))))).
