Show the proven property immediately in the README

README.md

@@ -10,19 +10,33 @@ for instances that undeployed contracts cannot have sent out any transactions.
 
 We also define a typeclass that captures what it means to satisfy our semantics.
 We exhibit two instances of this typeclass in
-[LocalBlockchain.v](theories/LocalBlockchain.v): one with depth-first execution
-order of smart contracts, and one with breadth-first execution order.
-
-In [Circulation.v](theories/Circulation.v) we prove a small sanity check for our
-semantics. Specifically we prove that the total sum of the money in the system
-is equal to the sum of the rewards handed out in blocks.
+[LocalBlockchain.v](theories/LocalBlockchain.v); these are essentially
+implementations of execution layers of modern blockchains. One is implemented
+with depth-first execution and the other with breadth-first execution order.
 
 In [Congress.v](theories/Congress.v) we implement the _Congress_ contract, a
 simplified version of the DAO, which does complex dynamic interactions with the
 blockchain and other contracts deployed on the blockchain. We specify and prove
 a property about this contract at the end of this file. This property is
 somewhat related to reentrancy in that it caps the number of transactions the
-Congress will make.
+Congress will make. The formal statement reads as follows:
+
+```coq
+Corollary congress_txs_after_block
+          {ChainBuilder : ChainBuilderType}
+          prev new header acts :
+  builder_add_block prev header acts = Some new ->
+  forall addr,
+    env_contracts new addr = Some (Congress.contract : WeakContract) ->
+    length (outgoing_txs (builder_trace new) addr) <=
+    num_acts_created_in_proposals (incoming_txs (builder_trace new) addr).
+```
+
+This is saying that, after adding a block, the number of transactions sent out
+by any deployed Congress is capped by the number of actions that were created in
+proposals up to this point. This is an approximation of the fact that any
+outgoing transaction should correspond to some proposal created and discussed in
+the past.
 
 In [Congress_Buggy.v](theories/Congress_Buggy.v) we try something different: we
 take the same contract as above, but introduce a reentrancy issue into it. We
@@ -30,9 +44,14 @@ then formally prove that this version of the Congress does _not_ satisfy the
 property proven for the other version. This is proven by using one of our
 implementations of our semantics and just asking Coq to compute.
 
+In [Circulation.v](theories/Circulation.v) we prove a small sanity check for our
+semantics. Specifically we prove that the total sum of the money in the system
+is equal to the sum of the rewards handed out in blocks.
+
 In [LocalBlockchainTests.v](theories/LocalBlockchainTests.v) we test that Coq is
 able to compute with the Congress by deploying it and interacting with it using
-one of our implementations of blockchains.
+one of our implementations of blockchains. We also specialize the proof shown
+about to our actual implementations of the execution layer described above.
 
 ## Building/Developing
 This repo uses the std++ library. This must be installed first and can be