Why do later passes not mess up earlier sorts?

Prove that after pass p, sorted for digit p+1 to last digit

Prove by induction over p

- True for p=1. Apply Stable sort to digit 1, sorted after pass
- Assume true for p=i, prove true for p=i+1
- After pass i, compare two numbers x and y
- If x appears before y then one of following conditions must be true
- for digit , then belongs before in sorted order
- for digit , then for rest of number, placed in that order in earlier pass, not swapped because use stable sort