Hash: Better explanation of P[M|C] in the proof of Lemma G

06-hash/hash.tex

@@ -330,7 +330,8 @@ Each term can be handled separately:
 $$\vbox{\halign{\hfil $\displaystyle{#}$&$\displaystyle{{}#}$\hfil&\quad #\hfil\cr
 	\Pr[M\mid\lnot C] &\le d/m^2 &by $(2,d)$-independence of~${\cal G}$ \cr
 	\Pr[\lnot C] &\le 1 &trivially \cr
-	\Pr[M\mid C] &\le d/m &because $(2,d)$-independence implies $(1,d)$-independence \cr
+	\Pr[M\mid C] &\le d/m &for $i_1\ne i_2$: the left-hand side is~0, \cr
+	{} & {} &for $i_1=i_2$: $(2,d)$-independence implies $(1,d)$-independence \cr
 	\Pr[C] &\le c/r &by $c$-universality of~${\cal F}$ \cr
 }}$$
 So $\Pr[M] \le d/m^2 + cd/mr$. We want to write this as $c' / m^2$, so