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## Homework Statement

I need to prove that different insertion orders of the same keys always gives us a different binary tree.

## Homework Equations

All obvious BST properties apply:

The left subtree of a node contains only nodes with keys less than the node's key.

The right subtree of a node contains only nodes with keys greater than the node's key.

Both the left and right subtrees must also be binary search trees.

There must be no duplicate nodes.

## The Attempt at a Solution

I don't exactly know how to formally prove this besides just showing a bunch of examples.

I think this is obvious because there aren't any duplicate keys therefore you will always have a unique layout of the tree.