chore: Apply suggestions from code review

Co-authored-by: Artem Storozhuk <[email protected]>

aptos/docs/src/components/proof_server.md

@@ -17,7 +17,7 @@ and leverages the [`lurk-lab/sphinx`](https://github.com/lurk-lab/sphinx) zkVM t
 
 In the design document of both the [epoch change proof](../design/epoch_change_proof.md) and
 the [inclusion proof](../design/inclusion_proof.md), we describe what each program has to prove. Most computations
-performed by the proof grams are directed towards cryptographic operations, such as verifying signatures on the block
+performed by the proof programs are directed towards cryptographic operations, such as verifying signatures on the block
 header.
 
 To accelerate those operations, we leverage some out-of-VM circuits called **pre-compiles** that are optimized for those

aptos/docs/src/design/epoch_change_proof.md

@@ -4,7 +4,7 @@ The Aptos consensus has (at any given time) a set of validators that are charged
 append them to the chain state.
 
 A set of given validators is updated at the last block of every epoch on the chain. An **epoch on the Aptos chain has a
-duration of 2 hours**. The light client needs to keep track of the hash of the current trusted validator set, which is
+duration of 2 hours**. The light client needs to keep track of the current trusted validator set hash, which is
 updated on every epoch change.
 
 For a given epoch \\(N\\) with a set of validators \\(V_n\\), it is expected to have a block for the transition to

aptos/docs/src/design/security.md

@@ -3,9 +3,9 @@
 ## Sphinx
 
 The [Sphinx](https://github.com/lurk-lab/sphinx) prover is a fork of [SP1](https://github.com/succinctlabs/sp1)
-and as such inherits many of its security design. The current release of Sphinx (`v1.0.0`) has backported all the
+and as such inherits a lot from its security design. The current release of Sphinx (`v1.0.0`) has backported all the
 upstream security fixes as of SP1 `v1.0.5-testnet`. We will continue to update Sphinx with backports of upstream
-security fixes and subsequent updates to both Sphinx and the Light Client will be made available as hotfixes.
+security fixes and subsequent updates to both Sphinx and the Light Client making them available as hotfixes.
 
 In terms of Sphinx-specific changes that require special attention, here is a non-exhaustive list of Sphinx
 AIR chips used for pre-compiles that are either not present in upstream SP1, or have had non-trivial changes: