Docs: fix capitals of section.

docs/algebra.tex

-\section{Algebraic Structures}
+\section{Algebraic structures}
 
 \subsection{OFE}
 

docs/base-logic.tex

-\section{Base Logic}
+\section{Base logic}
 \label{sec:base-logic}
 
 The base logic is parameterized by an arbitrary CMRA $\monoid$ having a unit $\munit$.

docs/constructions.tex

@@ -17,7 +17,7 @@ Note that in the definition of the carrier $\latert\cofe$, $\latertinj$ is a con
 $\latert(-)$ is a locally \emph{contractive} functor from $\OFEs$ to $\OFEs$.
 
 
-\subsection{Uniform Predicates}
+\subsection{Uniform predicates}
 
 Given a CMRA $\monoid$, we define the COFE $\UPred(\monoid)$ of \emph{uniform predicates} over $\monoid$ as follows:
 \begin{align*}

docs/ghost-state.tex

-\section{Extensions of the Base Logic}
+\section{Extensions of the base logic}
 
 In this section we discuss some additional constructions that we define within and on top of the base logic.
 These are not ``extensions'' in the sense that they change the proof power of the logic, they just form useful derived principles.

docs/program-logic.tex

@@ -5,7 +5,7 @@
 This section describes how to build a program logic for an arbitrary language (\cf \Sref{sec:language}) on top of the base logic.
 So in the following, we assume that some language $\Lang$ was fixed.
 
-\subsection{Dynamic Composeable Higher-Order Resources}
+\subsection{Dynamic composeable higher-order resources}
 \label{sec:composeable-resources}
 
 The base logic described in \Sref{sec:base-logic} works over an arbitrary CMRA $\monoid$ defining the structure of the resources.
@@ -101,7 +101,7 @@ We will typically leave the $M_i$ implicit when asserting ghost ownership, as th
 
 
 
-\subsection{World Satisfaction, Invariants, Fancy Updates}
+\subsection{World satisfaction, invariants, fancy updates}
 \label{sec:invariants}
 
 To introduce invariants into our logic, we will define weakest precondition to explicitly thread through the proof that all the invariants are maintained throughout program execution.
@@ -137,7 +137,7 @@ The following assertion states that an invariant with name $\iname$ exists and m
 \[ \knowInv\iname\prop \eqdef \ownGhost{\gname_{\textmon{Inv}}}
   {\authfrag \mapsingleton \iname {\aginj(\latertinj(\wIso(\prop)))}} \]
 
-\paragraph{Fancy Updates and View Shifts.}
+\paragraph{Fancy updates and view shifts.}
 Next, we define \emph{fancy updates}, which are essentially the same as the basic updates of the base logic ($\Sref{sec:base-logic}$), except that they also have access to world satisfaction and can enable and disable invariants:
 \[ \pvs[\mask_1][\mask_2] \prop \eqdef W * \ownGhost{\gname_{\textmon{En}}}{\mask_1} \wand \upd\diamond (W * \ownGhost{\gname_{\textmon{En}}}{\mask_2} * \prop) \]
 Here, $\mask_1$ and $\mask_2$ are the \emph{masks} of the view update, defining which invariants have to be (at least!) available before and after the update.
@@ -244,7 +244,7 @@ Still, just to give an idea of what view shifts ``are'', here are some proof rul
   {\FALSE \vs[\mask_1][\mask_2] \prop }
 \end{mathparpagebreakable}
 
-\subsection{Weakest Precondition}
+\subsection{Weakest preconditions}
 
 Finally, we can define the core piece of the program logic, the assertion that reasons about program behavior: Weakest precondition, from which Hoare triples will be derived.
 
@@ -439,7 +439,7 @@ We only give some of the proof rules for Hoare triples here, since we usually do
 %   {\knowInv\iname\propC \proves \hoare{\prop}{\expr}{\Ret\val.\propB}[\mask \uplus \set\iname]}
 \end{mathparpagebreakable}
 
-\subsection{Invariant Namespaces}
+\subsection{Invariant namespaces}
 \label{sec:namespaces}
 
 In \Sref{sec:invariants}, we defined an assertion $\knowInv\iname\prop$ expressing knowledge (\ie the assertion is persistent) that $\prop$ is maintained as invariant with name $\iname$.