PPT Slide

Basis: ( factorial 0 ) produces 1

( factorial 1 ) produces 1

by definition of the first two cases in the cond.

Hypothesis: Suppose ( factorial K )

correctly returns K!, K > 1

Inductive Part:

Then ( factorial < K + 1 > ) evaluates to

( * < K + 1 > ( factorial (- < K + 1 > 1 ) ) )

which will be

( * < K + 1 > ( factorial K ) )

or ( K + 1 ) * K! = ( K + 1 ) !