%   ORIGINAL: 'h4/thm/list/LIST_APPLY_o_'
% 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: !xs gs fs. 'h4/const/list/LIST_APPLY' ('h4/const/list/LIST_APPLY' ('h4/const/list/LIST_APPLY' ('h4/const/list/CONS' 'h4/const/combin/o' 'h4/const/list/NIL') fs) gs) xs = 'h4/const/list/LIST_APPLY' fs ('h4/const/list/LIST_APPLY' gs xs)
%   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: !xs gs fs. 'h4/const/list/LIST_APPLY' ('h4/const/list/LIST_APPLY' ('h4/const/list/LIST_APPLY' ('h4/const/list/CONS' 'h4/const/combin/o' 'h4/const/list/NIL') fs) gs) xs = 'h4/const/list/LIST_APPLY' fs ('h4/const/list/LIST_APPLY' gs xs)
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_3f11119,V_3f11115]: ![F, G]: (![X]: s(V_3f11115,happ(s(fun(V_3f11119,V_3f11115),F),s(V_3f11119,X))) = s(V_3f11115,happ(s(fun(V_3f11119,V_3f11115),G),s(V_3f11119,X))) => s(fun(V_3f11119,V_3f11115),F) = s(fun(V_3f11119,V_3f11115),G))).
fof('h4/thm/list/LIST_APPLY_o_', conjecture, ![A,C,B]: ![Xs, Gs, Fs]: s('h4/type/list/list'(A),'h4/const/list/LIST_APPLY'(s('h4/type/list/list'(fun(B,A)),'h4/const/list/LIST_APPLY'(s('h4/type/list/list'(fun(fun(B,C),fun(B,A))),'h4/const/list/LIST_APPLY'(s('h4/type/list/list'(fun(fun(C,A),fun(fun(B,C),fun(B,A)))),'h4/const/list/CONS'(s(fun(fun(C,A),fun(fun(B,C),fun(B,A))),'h4/const/combin/o'),s('h4/type/list/list'(fun(fun(C,A),fun(fun(B,C),fun(B,A)))),'h4/const/list/NIL'))),s('h4/type/list/list'(fun(C,A)),Fs))),s('h4/type/list/list'(fun(B,C)),Gs))),s('h4/type/list/list'(B),Xs))) = s('h4/type/list/list'(A),'h4/const/list/LIST_APPLY'(s('h4/type/list/list'(fun(C,A)),Fs),s('h4/type/list/list'(C),'h4/const/list/LIST_APPLY'(s('h4/type/list/list'(fun(B,C)),Gs),s('h4/type/list/list'(B),Xs)))))).
