Update README

README.md

@@ -6,9 +6,9 @@
 
 [![Continuous Integration - proof verification tests](https://github.com/HerodotusDev/cairo-verifier/actions/workflows/proof_verification_tests.yml/badge.svg)](https://github.com/HerodotusDev/cairo-verifier/actions/workflows/proof_verification_tests.yml)
 
-## Using Verifier contracts
+## Using Verifier contracts on Starknet
 
-To use the Verifier for verifying proofs on starknet, you need to generate calldata for your proof. The easiest way to do that is to use [Calldata Generator](https://github.com/HerodotusDev/integrity-calldata-generator). It also provides script for automatic transaction sending (proof verification is split into multiple transactions, for more information see [Split Verifier Architecture](/README.md#split-verifier-architecture)).
+To use the Verifier for verifying proofs on starknet, you need to generate calldata for your proof. The easiest way to do that is to use [Calldata Generator](https://github.com/HerodotusDev/integrity-calldata-generator). It also provides script for automatic transaction sending (proof verification is split into multiple transactions, for more information see [Split Verifier Architecture](#split-verifier-architecture)).
 
 ## Running locally
 
@@ -20,7 +20,7 @@ To build the Cairo Verifier, follow these steps:
 scarb build
 ```
 
-If you want to build for other layouts, refer to [Configure Verifier](/README.md#configure-verifier)
+If you want to build for other layouts, refer to [Configure Verifier](#configure-verifier)
 
 2. (Optional) Test the project to ensure everything works correctly:
 
@@ -39,25 +39,6 @@ cargo run --release --bin runner -- --program target/dev/cairo_verifier.sierra.j
 cargo run --release --bin runner -- --program target/dev/cairo_verifier.sierra.json -c cairo1 < examples/proofs/recursive/cairo1_example_proof.json
 ```
 
-<!-- ### Starknet Proof Verification
-
-To verify proofs on Starknet, proceed with the following steps:
-
-1. Prepare calldata of example proof for sncast:
-
-```bash
-cargo run --release --bin snfoundry_proof_serializer -- -c cairo0 < examples/proofs/recursive/cairo0_example_proof.json > examples/starknet/calldata
-```
-
-2. Call the function with calldata on the Starknet contract:
-
-```bash
-cd examples/starknet
-./1-verify-proof.sh 0x274d8165a19590bdeaa94d1dd427e2034462d7611754ab3e15714a908c60df7 calldata
-```
-
-[List of deployed Verifier Contracts](deployed_contracts.md) -->
-
 ### Configure Verifier
 
 By default, the verifier is configured for monolith version, recursive layout and keccak hash for verifier unfriendly commitment layers. You can easily change that by using scarb's features:
@@ -100,4 +81,9 @@ Since verifier can be configured in many ways and some parts of the logic change
 
 After proof is verified, `FactRegistered` event is emitted which contains `fact_hash`, `verification_hash`, `security_bits` and `settings`. `fact_hash` is a value that represents proven program and its output (formally `fact_hash = poseidon_hash(program_hash, output_hash)`). Remember that registration of some `fact_hash` doesn't necessary mean that it has been verified by someone with secure enough proof. You always need to check `security_bits` and `settings` which is part of `verification_hash` (formally `verification_hash = poseidon_hash(fact_hash, security_bits, settings)`).
 
+`FactRegistry` provides two methods for checking verified proofs:
+
+-   `get_verification(verification_hash)`
+-   `get_all_verifications_for_fact_hash(fact_hash)`
+
 FactRegistry contract is trustless which means that owner of the contract can't override or change any existing behavior, they can only add new verifiers. Proxy contract on the other hand is upgradable, so every function can be changed or removed. It has the advantage of having all future updates of the verifier logic without having to replace the address of FactRegistry contract.