diff git a/README.md b/README.md
index ffcab1dd92b0765d23b838d6afa70089ee06fea8..dc253bc8e68d50ea3f6168da85c0a942163689fd 100644
 a/README.md
+++ b/README.md
@@ 16,14 +16,15 @@ In order to build, install the above dependencies and then run
## Theory of Actris
The theory of Actris (semantics of channels, the CPS model, and the proof rules)
+The theory of Actris (semantics of channels, the model, and the proof rules)
can be found in the directory [theories/channel](theories/channel). The files
correspond to the following parts of the paper:
 [theories/channel/channel.v](theories/channel/channel.v): The definitional
semantics of bidirectional channels in terms of Iris's HeapLang language.
 [theories/channel/proto_model.v](theories/channel/proto_model.v): The CPS
 model of Dependent Separation Protocols over arbitrary BIlogics.
+ [theories/channel/proto_model.v](theories/channel/proto_model.v): The
+ construction of the model of Dependent Separation Protocols as the solution of
+ a recursive domain equation.
 [theories/channel/proto_channel.v](theories/channel/proto_channel.v): The
instantiation of protocols with the Iris logic, definition of the connective `↣`
for channel endpoint ownership, and lemmas corresponding to the Actris proof rules.
@@ 44,28 +45,18 @@ correspond to the following parts of the paper:
## Notation
The notation for Dependent Separation Protocols differ between the
mechanisation and the paper.
+The notation for Dependent Separation Protocols differ between the paper and
+the Coq mechanization:
The paper uses the following notation:

 Send: ! x_1 .. x_n < v > { P } . prot
 Recv: ? x_1 .. x_n < v > { P } . prot
 End: end
 Select: prot_1 {Q_1} ⊕ {Q_2} prot_2
 Branch: prot_1 {Q_1} & {Q_2} prot_2
 Append: prot_1 · prot_2
 Dual: An overlined protocol

The mechanisation uses the following notation:

 Send: x_1 .. x_n, MSG v {{ P }} ; prot
 Recv: x_1 .. x_n, MSG v {{ P }} ; prot
 End: END
 Select: prot_1 <{Q_1} + {Q_2}> prot_2
 Branch: prot_1 <{Q_1} & {Q_2}> prot_2
 Append: prot_1 <++> prot_2
 Dual: Nothing
+  Paper  Coq mechanization 
+
+ Send  `! x_1 .. x_n { P }. prot`  ` x_1 .. x_n, MSG v {{ P }}; prot` 
+ Recv  `? x_1 .. x_n { P }. prot`  ` x_1 .. x_n, MSG v {{ P }}; prot` 
+ End  `end`  `END` 
+ Select  `prot_1 {Q_1}⊕{Q_2} prot_2`  `prot_1 <{Q_1}+{Q_2}> prot_2` 
+ Branch  `prot_1 {Q_1}&{Q_2} prot_2`  `prot_1 <{Q_1}&{Q_2}> prot_2` 
+ Append  `prot_1 · prot_2`  `prot_1 <++> prot_2` 
+ Dual  An overlined protocol  No notation 
## Weakest preconditions and Coq tactics
@@ 188,13 +179,11 @@ of Actris and the formalization in Coq, that are briefly discussed here.
2. the higherorder ghost state used for ownership of protocols, and
3. the opening of the protocol invariant.
 **Subtyping relation in c↣ prot**
+ **Protocol subtyping**
+
+ The mechanization has introduced the notion of "protocol subtyping", which
+ allows one to strengthen/weaken the predicates of sends/receives, respectively.
+ This achieved using the relation `iProto_le p p'`, and the additional rule
+ `c ↣ p ∗ iProto_le p p' ∗ c ↣ p'`. To support "protocol subtyping", the
+ definition of `c ↣ p` in the model is changed to be closed under `iProto_le`.
 The mechanisation has introduced the notion of subtyping, which allows one to
 strengten/weaken the predicates of sends/receives respectively. In particular
 this means that the endpoint ownership has been extended with `iProto_le p p'`,
 where `p'` is the original protocol used in the ghost state, and `p` is the
 protocol denoted by the ownership `c↣ prot`. The effect of this is that the
 user can update his own view of the protocol, as long as it is consistent
 with the original protocol in the invariant. As such the fundamental aspect of
 the ownership still align with that of the paper.
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