%   ORIGINAL: 'h4/thm/rich_list/APPEND_ASSOC_CONS_'
% 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: !l1 h l2 l3. 'h4/const/list/APPEND' ('h4/const/list/APPEND' l1 ('h4/const/list/CONS' h l2)) l3 = 'h4/const/list/APPEND' l1 ('h4/const/list/CONS' h ('h4/const/list/APPEND' l2 l3))
%   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: !l1 h l2 l3. 'h4/const/list/APPEND' ('h4/const/list/APPEND' l1 ('h4/const/list/CONS' h l2)) l3 = 'h4/const/list/APPEND' l1 ('h4/const/list/CONS' h ('h4/const/list/APPEND' l2 l3))
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_3f57311,V_3f57307]: ![F, G]: (![X]: s(V_3f57307,happ(s(fun(V_3f57311,V_3f57307),F),s(V_3f57311,X))) = s(V_3f57307,happ(s(fun(V_3f57311,V_3f57307),G),s(V_3f57311,X))) => s(fun(V_3f57311,V_3f57307),F) = s(fun(V_3f57311,V_3f57307),G))).
fof('h4/thm/rich_list/APPEND_ASSOC_CONS_', conjecture, ![A]: ![L1, H, L2, L3]: s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),L2))))),s('h4/type/list/list'(A),L3))) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L2),s('h4/type/list/list'(A),L3)))))))).
