Splay: Fixed English

02-splay/splay.tex

@@ -73,7 +73,7 @@ The amortized cost of the full \alg{Splay} is a~sum of amortized costs of the in
 Let $r_1(x),\ldots,r_t(x)$ denote the rank of~$x$ after each step and $r_0(x)$ the rank
 before the first step.
 
-We will use the following claim, which will be proved in the rest of this section:
+We will use the following claim, which will be proven in the rest of this section:
 
 {\narrower\claim{
 	The amortized cost of the $i$-th step is at most $3r_i(x) - 3r_{i-1}(x)$,
@@ -385,7 +385,7 @@ number of nodes in the tree during the sequence.}
 \def\rmin{r_{\rm min}}
 
 Splay trees have surprisingly many interesting properties. Some of them can be
-proved quite easily by generalizing the analysis of \em{Splay} by putting different
+proven quite easily by generalizing the analysis of \em{Splay} by putting different
 weights on different nodes.
 
 We will assign a~positive real \em{weight} $w(v)$ to each node~$v$. The size of