%   ORIGINAL: 'h4/thm/rich_list/EVERY2_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: !l4 l3 l2 l1 R. 'h4/const/list/LIST_REL' R l1 l2 /\ 'h4/const/list/LIST_REL' R l3 l4 <=> 'h4/const/list/LIST_REL' R ('h4/const/list/APPEND' l1 l3) ('h4/const/list/APPEND' l2 l4) /\ 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 /\ 'h4/const/list/LENGTH' l3 = 'h4/const/list/LENGTH' l4
%   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: !l4 l3 l2 l1 R. 'h4/const/list/LIST_REL' R l1 l2 /\ 'h4/const/list/LIST_REL' R l3 l4 <=> 'h4/const/list/LIST_REL' R ('h4/const/list/APPEND' l1 l3) ('h4/const/list/APPEND' l2 l4) /\ 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 /\ 'h4/const/list/LENGTH' l3 = 'h4/const/list/LENGTH' l4
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_3f58086,V_3f58082]: ![F, G]: (![X]: s(V_3f58082,happ(s(fun(V_3f58086,V_3f58082),F),s(V_3f58086,X))) = s(V_3f58082,happ(s(fun(V_3f58086,V_3f58082),G),s(V_3f58086,X))) => s(fun(V_3f58086,V_3f58082),F) = s(fun(V_3f58086,V_3f58082),G))).
fof('h4/thm/rich_list/EVERY2_APPEND_', conjecture, ![A,B]: ![L4, L3, L2, L1, R]: ((p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2)))) & p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),s('h4/type/list/list'(A),L3),s('h4/type/list/list'(B),L4))))) <=> (p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L3))),s('h4/type/list/list'(B),'h4/const/list/APPEND'(s('h4/type/list/list'(B),L2),s('h4/type/list/list'(B),L4)))))) & (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),L2))) & s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L3))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),L4))))))).
