https://alloy.readthedocs.io/en/latest/language/signatures.html#relations

>[!note]
>Node.prox' = Node.prox
!=
all n:Node | n.prox' = n.prox
= 
prox' = prox

>[!note]
>some b: Bucket | ...


```c
// Recall the hash table Alloy model,
// now with mutable lists inside the buckets.

sig Bucket {
	var head : lone Node
}
sig Node {
	key : one Key,
	var prox : lone Node
}
sig Key {
	hash : one Hash
}
sig Hash {}

// Specify the operation of inserting a node
// in the hash table. The node should be 
// inserted at the head of a bucket.
// If the operation only works well when the
// hash of the new node does not exist in the
// table you get Two points. If it always 
// works well you get Five points. Use the
// respective commands to check how many
// points you have.


pred insert[n : Node] {
	always n in ( Bucket.head + Bucket.head.prox)
	always n in Bucket.head or n in Node.prox

  	//if hash empty -> node to head of bucket
	n.key.hash not in Hash implies
	(
      lone b:Bucket | b.head = none implies b.head' = n
  	)
  	//if hash empty -> bucket of desired hash, add to next
  	n.key.hash in Hash implies
  	(
      lone b: Bucket | b.head.key.hash = n.key.hash | b.head.*prox = n
  	)
}



```