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diff --git a/Core2Core.tex b/Core2Core.tex
index 1f258d3..b404a03 100644
--- a/Core2Core.tex
+++ b/Core2Core.tex
@@ -260,6 +260,9 @@ is specified as a number of conditions (above the horizontal line) and a
 number of conclusions (below the horizontal line). The details of using
 this notation are still a bit fuzzy, so comments are welcom.
 
+TODO: Formally describe the "apply to every (sub)expression" in terms of
+rules with full transformations in the conditions.
+
 \subsection{η-abstraction}
 This transformation makes sure that all arguments of a function-typed
 expression are named, by introducing lambda expressions. When combined with
@@ -600,6 +603,38 @@ translatable. A user-defined function is any other function.
 TODO: The above definition looks too complicated... Can we find
 something more concise?
 
+\subsection{Cast propagation}
+This transform pushes casts down into the expression as far as possible.
+\subsection{Let recursification}
+This transform makes all lets recursive.
+\subsection{Let simplification}
+This transform makes the result value of all let expressions a simple
+variable reference.
+\subsection{Let flattening}
+This transform turns two nested lets (\lam{let x = (let ... in ...) in
+...}) into a single let.
+\subsection{Simple let binding removal}
+This transforms inlines simple let bindings (\eg a = b).
+\subsection{Function inlining}
+This transform inlines let bindings of a funtion type. TODO: This should
+be generelized to anything that is non representable at runtime, or
+something like that.
+\subsection{Scrutinee simplification}
+This transform ensures that the scrutinee of a case expression is always
+a simple variable reference.
+\subsection{Case binder wildening}
+This transform replaces all binders of a each case alternative with a
+wild binder (\ie, one that is never referred to). This will possibly
+introduce a number of new "selector" case statements, that only select
+one element from an algebraic datatype and bind it to a variable.
+\subsection{Case value simplification}
+This transform simplifies the result value of each case alternative by
+binding the value in a let expression and replacing the value by a
+simple variable reference.
+\subsection{Case removal}
+This transform removes any case statements with a single alternative and
+only wild binders.
+
 \subsection{Example sequence}
 
 This section lists an example expression, with a sequence of transforms