Allow narrowing generic type to single element of union type

It is a fairly common pattern to create a set of generic components, and then to use the generic component type within the system. Currently, typescript has an issue handling cases where some values of a generic component depend on others.

TypeScript Version: 2.4.0 / nightly (2.5.0-dev.201xxxxx)
2.4
Code

let index = {
    a: {
        arg: 'a',
        fn: (a: string) => {a.toUpperCase()}
    },
    b: {
        arg: 1,
        fn: (b: number) => {b + 1}
    }
}

let runFn= <K extends keyof (typeof index)>(key: K) => {
    let i = index[key]
    let arg = i.arg
    let fn = i.fn
    fn(arg) // Error: compiler doesn't understand that fn and arg will match
}

Expected behavior:
No error, since we know that arg and fn are pulled off of the same map entry.

Actual behavior:
Error: cannot invoke expression whose type lacks a call signature

Start by reproducing the provided TypeScript 2.4 example and confirm the error when invoking fn(arg). Then trace the type-checking path for indexed access through a generic key and dependent union members; done means the example compiles without weakening type safety.