%   ORIGINAL: 'h4/thm/rich_list/IS_PREFIX_e2'
% 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: !x1 l1 x2 l2. 'h4/const/list/isPREFIX' ('h4/const/list/CONS' x2 l2) ('h4/const/list/CONS' x1 l1) <=> x1 = x2 /\ 'h4/const/list/isPREFIX' l2 l1
%   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: !x1 l1 x2 l2. 'h4/const/list/isPREFIX' ('h4/const/list/CONS' x2 l2) ('h4/const/list/CONS' x1 l1) <=> x1 = x2 /\ 'h4/const/list/isPREFIX' l2 l1
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_3f51961,V_3f51957]: ![F, G]: (![X]: s(V_3f51957,happ(s(fun(V_3f51961,V_3f51957),F),s(V_3f51961,X))) = s(V_3f51957,happ(s(fun(V_3f51961,V_3f51957),G),s(V_3f51961,X))) => s(fun(V_3f51961,V_3f51957),F) = s(fun(V_3f51961,V_3f51957),G))).
fof('h4/thm/rich_list/IS_PREFIX_e2', conjecture, ![A]: ![X1, L1, X2, L2]: (p(s(bool,'h4/const/list/isPREFIX'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X2),s('h4/type/list/list'(A),L2))),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X1),s('h4/type/list/list'(A),L1)))))) <=> (s(A,X1) = s(A,X2) & p(s(bool,'h4/const/list/isPREFIX'(s('h4/type/list/list'(A),L2),s('h4/type/list/list'(A),L1))))))).
