proposition: Theorem remove_decreases_count: forall (s : bag), leb (count 0 (remove_one 0 s)) (count 0 s) = true.
proof: Proof. MProof. Admitted. Fixpoint nth_bad (l:natlist) (n:nat) : nat := match l with | nil => 42 | a :: l' => match beq_nat n O with | true => a | false => nth_bad l' (pred n) end end. Inductive natoption : Type := | Some : nat -> natoption | None : natoption. Fixpoint nth_error (l:natlist) (n:nat) : natoption := match l with | nil => None | a :: l' => match beq_nat n O with | true => Some a | false => nth_error l' (pred n) end end. Example test_nth_error1 : nth_error [4;5;6;7] 0 = Some 4. MProof. reflexivity. Qed.