Prove Theorem 8.5.1
is a partial order relation.
Let be a set with a partial order relation and let be a set of strings over .
A relation is defined as follows:
For any two strings in where are positive integers.
To prove is reflexive:
Let be any string in .
If , then .
Suppose . Let .
Then for all .
Hence, is reflexive.
To prove is antisymmetric:
Let such that .
Suppose be the least positive integer such that .
Since is partial order relation on , therefore implies that
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