In this lecture, we explain precisely when the formula is and when we can. U Minimal element of a set . Finite chain property . We will see that having only finite chains has something to do with math induction. E has the same number of left and right parentheses.
Proof is by induction over the structure of expressions.
Consider an arbitrary expression E Case E is an integer. An integer has no parentheses, so P.E holds. By the induction hypotheses, P.E0 and P.E1 hold. Thus, E0 and E1 each have the same number of left and right parentheses. By the induction hypotheses, P.E holds.