15-399 Constructive Logic
Lecture 6: Subject Reduction
After reviewing proof terms and introducing their concrete syntax
needed for the proof checker, we study properties of proof terms.
We recall the substitution property of hypothetical
judgments and extend it to encompass proof terms. The then prove
If M : A and M ==> M' then M' : A.
The proof technique is proof by cases. We then generalize to
allow reduction at an arbitrary subterm position. Then the
proof requires structural induction, one of the main proof
techniques in this domain.