+[@Hind | cases (a==x) normalize // @Hind]
+qed.
+
+lemma decidable_sublist:∀S,l1,l2.
+ (sublist S l1 l2) ∨ ¬(sublist S l1 l2).
+#S #l1 #l2 elim l1
+ [%1 #a normalize in ⊢ (%→?); #abs @False_ind /2/
+ |#a #tl * #subtl
+ [cases (true_or_false (memb S a l2)) #memba
+ [%1 whd #x #membx cases (orb_true_l … membx)
+ [#eqax >(\P eqax) // |@subtl]
+ |%2 @(not_to_not … (eqnot_to_noteq … true memba)) #H1 @H1 @memb_hd
+ ]
+ |%2 @(not_to_not … subtl) #H1 #x #H2 @H1 @memb_cons //
+ ]
+ ]