%   ORIGINAL: 'h4/thm/list/ALL_DISTINCT_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: !l1 l2. 'h4/const/list/ALL_DISTINCT' ('h4/const/list/APPEND' l1 l2) <=> 'h4/const/list/ALL_DISTINCT' l1 /\ 'h4/const/list/ALL_DISTINCT' l2 /\ (!e. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l1) ==> ~'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l2))
%   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 l2. 'h4/const/list/ALL_DISTINCT' ('h4/const/list/APPEND' l1 l2) <=> 'h4/const/list/ALL_DISTINCT' l1 /\ 'h4/const/list/ALL_DISTINCT' l2 /\ (!e. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l1) ==> ~'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l2))
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_3f7740,V_3f7736]: ![F, G]: (![X]: s(V_3f7736,happ(s(fun(V_3f7740,V_3f7736),F),s(V_3f7740,X))) = s(V_3f7736,happ(s(fun(V_3f7740,V_3f7736),G),s(V_3f7740,X))) => s(fun(V_3f7740,V_3f7736),F) = s(fun(V_3f7740,V_3f7736),G))).
fof('h4/thm/list/ALL_DISTINCT_APPEND_', conjecture, ![A]: ![L1, L2]: (p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L2)))))) <=> (p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(A),L1)))) & (p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(A),L2)))) & ![E]: (p(s(bool,'h4/const/bool/IN'(s(A,E),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L1)))))) => ~ (p(s(bool,'h4/const/bool/IN'(s(A,E),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L2)))))))))))).
