On Monday, July 15, 2013 9:50:39 PM UTC+1, Dan Christensen wrote:
> 1. Base case: > > Double induction: Prove P(1,1) > > 2. Inductive step: > > Double induction: For x, y in N, assume P(x,y) and prove P(x+1,y) and P(x,y+1). > > Comments?
That would indeed prove P (x, y) for all pairs x, y. However, it may be impossible to prove one of these. For example, I might be able to prove P (x, y) implies P (x+1, y), and I might only be able to prove that if P (x, y) is true for all integers y, then P (x + 1, y) is true.