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Can you clarify your expectations? Do you want the provider opt to be available as a property on the class?

yes only because thats what it looked like it was a output of in document

// Create an EKS cluster with the default configuration.
const cluster = new eks.Cluster("my-cluster");

// skipping like 15 lines of code
       }
    },
}, { provider: cluster.provider });

In that case, provider is an opt, not an arg. It's a member of the object passed in as the 3rd parameter, not the 2nd parameter. provider is not a member of eks.Cluster, it's a member of ResourceOptions.