Prove that the greedy algorithm to remove k digits from a n-digit positive integer is optimal

Question

Given a positive n-digit integer, such as 1214532 (n=7), remove k digits (for example k=4) such that the resulting integer is the smallest one.

A greedy algorithm for this would keep removing digits such that the resulting integer is the smallest. For the above example:

Step 1: Remove 2 => 114532
Step 2: Remove 5 => 11432
Step 3: Remove 4 => 1132
Step 4: Remove 3 => 112

Can you prove that this algorithm is optimal (i.e. the final integer is the smallest possible)? Or if it is not, show a counterexample?

Thanks!