In contrast, an indirect proof may begin with certain hypothetical scenarios and then proceed to eliminate the uncertainties in each of these scenarios until an inescapable conclusion is forced. For example instead of showing directly p → q, one proves its contrapositive ~q → ~p (one assumes ~q and shows that it leads to ~p). Since p → q and ~q → ~p are equivalent by the principle of transposition, one has indirectly proved p → q. Proof methods that are not direct include Proof by contradiction, Proof by exhaustion, Proof by infinite descent and Proof by induction.
What follows is a simple, direct proof that the sum of two even integers is itself an even number.
Consider two even integers and . Since they are even, they can be written as and respectively for integers and . Then the sum . From this it is clear has 2 as a factor and therefore is even, so the sum of any two even integers is even.