Use the result of problem 3.5 to prove that, in every finite set of distinct expressions, such as r and s in (3.5), there is an expression that is lexicographically smaller than all the others....

Use the result of problem 3.5 to prove that, in every finite set of distinct expressions, such as r and s in (3.5), there is an expression that is lexicographically smaller than all the others.

Problem 3.5

Prove: If
is lexicographically smaller than
 and if s is lexicographically smaller than
 than r is lexicographically smaller than t.