Proof of Proof: Prove that the avid algorithm to eliminate k digits of a positive integer of n digits is optimal

Given a positive integer of n digits, such as 1214532 (n = 7), delete k digits (for example, k = 4) so ​​that the resulting integer is the smallest.

A greedy algorithm for this would still eliminate digits, so that the resulting integer is the smallest. For the previous example:

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

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

Thank you!