Fix typo and syntax

specs/introduction.md

@@ -1,6 +1,6 @@
 # ZKEVM Introduction
 
-At the moment every node on ethereum has to validate every transaction in the ethereum virtual machine. This means that every transaction adds work that everyone needs to do to verify ethereums history. Worse still is that each transaction needs to be verified by every new node. Which means the amout of work a new node needs to do the sync the network is growing constantly. We want to build a proof of validity for the Ethereum blocks to avoid this. Are two goals are
+At the moment every node on ethereum has to validate every transaction in the ethereum virtual machine. This means that every transaction adds work that everyone needs to do to verify ethereums history. Worse still is that each transaction needs to be verified by every new node. Which means the amount of work a new node needs to do the sync the network is growing constantly. We want to build a proof of validity for the Ethereum blocks to avoid this. There are two goals.
 
 1. Make a zkrollup that supports smart contracts
 2. Create a proof of validity for every Ethereum block
@@ -10,6 +10,6 @@ This means making a proof of validity for the EVM + state reads  / writes + sign
 To simplify we separate our proofs into two components.
 
 1. **State proof**: State/memory/stack ops have been performed correctly. This does not check if the correct location has been read/written. We allow our prover to pick any location here and in the EVM proof confirm it is correct.
-2. **EVM proof**: This checks that the correct opcode is called at the correct time. It checks the validity of these opcodes. It also confirms that for each of these opcodes the state proof performed the correct operation.
+2. **EVM proof**: This checks that the correct opcode is called at the correct time. It checks the validity of these opcodes. It also confirms that for each of these opcodes and the state proof performed the correct operation.
 
-Only after verifying both proofs are we confident that that Ethereum block is executed correctly.
+Only after verifying both proofs are valid, we confident that Ethereum block is executed correctly.

specs/state-proof.md

@@ -1,6 +1,6 @@
 # State Proof
 
-The state proof helps EVM proof to check all the random read-write access records are valid, throgh grouping them by their unique index first, and then sorting them by order of access. We call the order of access `GlobalCounter`, which counts the number of access records and also serves as an unique identifier for a record. When state proof is generated, the `BusMapping` is also produced and will be shared to EVM proof as a lookup table.
+The state proof helps EVM proof to check all the random read-write access records are valid, through grouping them by their unique index first, and then sorting them by order of access. We call the order of access `GlobalCounter`, which counts the number of access records and also serves as an unique identifier for a record. When state proof is generated, the `BusMapping` is also produced and will be shared to EVM proof as a lookup table.
 
 ## Random Read-Write Data