Proof:Weak induction principle with n-1 is equivalent to weak induction
From CS2800 wiki
Suppose you have an inductive proof in the following style:
To prove weak induction, you can prove and prove for an arbitrary , assuming .by
But you are only willing to accept the basic weak induction principle:
To prove "weak induction, you must prove (this is often called the base case), and then you must prove for an arbitrary , assuming (this is called the inductive step)." using
You can systematically convert from the first style to the second:
Proof: By changing variable names
Assume the statements that are given in the claim; we will show and for an arbitrary , assuming .
is easy: it was given to us as assumption 1.