hello,

proving some predicate $\displaystyle A$ over the naturals $\displaystyle N$.

if the following statement holds for my base case, say $\displaystyle n = 1$

$\displaystyle A(n) \wedge A(n + 1)$

and i then assume it to hold for all $\displaystyle n \epsilon N$,

then i can also assume that $\displaystyle A(n)$ holds for all $\displaystyle n$.

i can hence take my inductive hypothesis as

$\displaystyle A(n) \rightarrow A(n + 1)$

but i already know that $\displaystyle A(n + 1)$ holds for all n.

this has got to be cheating right?

thanks for any pointers