> Aztec.nr API reference, v6.0.0 (mainnet and testnet). Index: https://docs.aztec.network/aztec-nr-api/v6.0.0/llms.txt

# Function check_non_membership

Module: `noir_aztec::protocol::merkle_tree::membership`

```rust
pub fn check_non_membership<let TREE_HEIGHT: u32, LEAF_PREIMAGE, VALUE>(
    key: Field,
    low_leaf_preimage: LEAF_PREIMAGE,
    low_leaf_membership_witness: MembershipWitness<TREE_HEIGHT>,
    tree_root: Field,
) -> (bool, bool, bool)
where
    LEAF_PREIMAGE: IndexedTreeLeafPreimage<VALUE>
```

Check a key's non-existence in the indexed tree with the given `tree_root`. `low_leaf_preimage` is the preimage for the low leaf of the key. The key should be larger than the low leaf's key, and smaller than the low leaf's next key. `low_leaf_membership_witness` is a hint to prove that the low leaf exists in the tree with the given `tree_root`.

Returns:

- non_existence: `true` if the key does not exist in the tree, `false` otherwise.
- is_valid_low_leaf: `true` if the key is in range of the low leaf, `false` otherwise.
- low_leaf_exists: `true` if the low leaf exists in the tree, `false` otherwise.