Delete redundant "The notation ..." in Notation section.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>

protocol/protocol.tex

@@ -900,12 +900,12 @@ one valid \nullifier, and so attempting to spend a \note twice would reveal the
 
 \nsection{Notation}
 
-The notation $\bit$ means the type of bit values, i.e.\ $\setof{0, 1}$.
+$\bit$ means the type of bit values, i.e.\ $\setof{0, 1}$.
 
-The notation $\Nat$ means the type of nonnegative integers. $\PosInt$
+$\Nat$ means the type of nonnegative integers. $\PosInt$
 means the type of positive integers. $\Rat$ means the type of rationals.
 
-The notation $x \typecolon T$ is used to specify that $x$ has type $T$.
+$x \typecolon T$ is used to specify that $x$ has type $T$.
 A cartesian product type is denoted by $S \times T$, and a function type
 by $S \rightarrow T$. An argument to a function can determine other argument
 or result types.
@@ -921,25 +921,25 @@ written as subscripts, e.g.\ if $x \typecolon X$, $y \typecolon Y$, and
 $f \typecolon X \times Y \rightarrow Z$, then an invocation of
 $f(x, y)$ can also be written $f_x(y)$.
 
-The notation $\typeexp{T}{\ell}$, where $T$ is a type and $\ell$ is an integer,
+$\typeexp{T}{\ell}$, where $T$ is a type and $\ell$ is an integer,
 means the type of sequences of length $\ell$ with elements in $T$. For example,
 $\bitseq{\ell}$ means the set of sequences of $\ell$ bits.
 
-The notation $\length(S)$ means the length of (number of elements in) $S$.
+$\length(S)$ means the length of (number of elements in) $S$.
 
-The notation $T \subseteq U$ indicates that $T$ is an inclusive subset or subtype of $U$.
+$T \subseteq U$ indicates that $T$ is an inclusive subset or subtype of $U$.
 
 $\byteseqs$ means the set of bit sequences constrained to be of length
 a multiple of 8 bits.
 
-The notation $\hexint{}$ followed by a string of \textbf{boldface} hexadecimal
+$\hexint{}$ followed by a string of \textbf{boldface} hexadecimal
 digits means the corresponding integer converted from hexadecimal.
 
-The notation $\ascii{...}$ means the given string represented as a
+$\ascii{...}$ means the given string represented as a
 sequence of bytes in US-ASCII. For example, $\ascii{abc}$ represents the
 byte sequence $[\hexint{61}, \hexint{62}, \hexint{63}]$.
 
-The notation $a..b$, used as a subscript, means the sequence of values
+$a..b$, used as a subscript, means the sequence of values
 with indices $a$ through $b$ inclusive. For example,
 $\AuthPublicNew{\allNew}$ means the sequence $[\AuthPublicNew{\mathrm{1}},
 \AuthPublicNew{\mathrm{2}}, ...\,\AuthPublicNew{\NNew}]$.
@@ -948,55 +948,55 @@ this specification uses 1-based indexing and inclusive ranges,
 notwithstanding the compelling arguments to the contrary made in
 \cite{EWD-831}.)
 
-The notation $\range{a}{b}$ means the set or type of integers from $a$ through
+$\range{a}{b}$ means the set or type of integers from $a$ through
 $b$ inclusive.
 
-The notation $\listcomp{f(x) \for x \from a \upto b}$ means the sequence
+$\listcomp{f(x) \for x \from a \upto b}$ means the sequence
 formed by evaluating $f$ on each integer from $a$ to $b$ inclusive, in
 ascending order. Similarly, $\listcomp{f(x) \for x \from a \downto b}$ means
 the sequence formed by evaluating $f$ on each integer from $a$ to $b$
 inclusive, in descending order.
 
-The notation $a\,||\,b$ means the concatenation of sequences $a$ then $b$.
+$a\,||\,b$ means the concatenation of sequences $a$ then $b$.
 
-The notation $\concatbits(S)$ means the sequence of bits obtained by
+$\concatbits(S)$ means the sequence of bits obtained by
 concatenating the elements of $S$ viewed as bit sequences. If the
 elements of $S$ are byte sequences, they are converted to bit sequences
 with the \emph{most significant} bit of each byte first.
 
-The notation $\sorted(S)$ means the sequence formed by sorting the elements
+$\sorted(S)$ means the sequence formed by sorting the elements
 of $S$.
 
-The notation $\GF{n}$ means the finite field with $n$ elements, and
+$\GF{n}$ means the finite field with $n$ elements, and
 $\GFstar{n}$ means its group under multiplication.
 $\GF{n}[z]$ means the ring of polynomials over $z$ with coefficients
 in $\GF{n}$.
 
-The notation $a \mult b$ means the result of multiplying $a$ and $b$.
+$a \mult b$ means the result of multiplying $a$ and $b$.
 This may refer to multiplication of integers, rationals, or
 finite field elements according to context.
 
-The notation $a^b$, for $a$ an integer or finite field element and
+$a^b$, for $a$ an integer or finite field element and
 $b$ an integer, means the result of raising $a$ to the exponent $b$.
 
-The notation $a \bmod q$, for $a \typecolon \Nat$ and $q \typecolon \PosInt$,
+$a \bmod q$, for $a \typecolon \Nat$ and $q \typecolon \PosInt$,
 means the remainder on dividing $a$ by $q$.
 
-The notation $a \xor b$ means the bitwise-exclusive-or of $a$ and $b$,
+$a \xor b$ means the bitwise-exclusive-or of $a$ and $b$,
 and $a \band b$ means the bitwise-and of $a$ and $b$. These are
 defined either on integers or bit sequences according to context.
 
-The notation $\vsum{i=1}{\mathrm{N}} a_i$ means the sum of $a_{\allN{}}$.\;
+$\vsum{i=1}{\mathrm{N}} a_i$ means the sum of $a_{\allN{}}$.\;
 $\vxor{i=1}{\mathrm{N}} a_i$ means the bitwise exclusive-or of $a_{\allN{}}$.
 
 The binary relations $<$, $\leq$, $=$, $\geq$, and $>$ have their conventional
 meanings on integers and rationals, and are defined lexicographically on
 sequences of integers.
 
-The notation $\floor{x}$ means the largest integer $\leq x$.
+$\floor{x}$ means the largest integer $\leq x$.
 $\ceiling{x}$ means the smallest integer $\geq x$.
 
-The notation $\bitlength(x)$, for $x \typecolon \Nat$, means the smallest integer
+$\bitlength(x)$, for $x \typecolon \Nat$, means the smallest integer
 $\ell$ such that $2^\ell > x$.
 
 The symbol $\bot$ is used to indicate unavailable information or a failed decryption.