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 (see law of excluded middle), "p" ⇒ "q" is indirectly proved. Proof methods that are not direct include proof by contradiction, including proof by infinite descent. Direct proof methods include proof by exhaustion and proof by induction.