Intersection breaks generic key field inference

[jeremybparagon]

TypeScript Version: 3.1.0-dev.20180810

Code

const f = <T extends { [K0 in K]: string; } & { cool: string; }, K extends keyof T>(t: T, k: K) =>
{
  const s: string = t[k];
};

Expected behavior: Successful compilation

Actual behavior: I get the following error:

error TS2322: Type 'T[K]' is not assignable to type 'string'.

     const s: string = t[k];
           ~

Playground Link: Link

Additional Notes: This compiles successfully (link):

const f = <T extends { [K0 in K]: string; } & { cool: string; }, K extends keyof T>(t: T, k: K) =>
{
  const s: string = t['cool'];
};

as does this (link):

const f = <T extends { [K0 in K]: string; }, K extends keyof T>(t: T, k: K) =>
{
  const s: string = t[k];
};

[ahejlsberg]

The issue here is that we're not examining all constraints of indexed access types in type relations, rather we jump straight to base constraints.

In exploring the issue I also discovered that this errors where it shouldn't:

const f = <T extends { [P in K | "cool"]: string; }, K extends keyof T>(t: T, k: K) =>
{
    const s: string = t[k];
    t.cool;  // Error, but shouldn't be
};

I'll put up a PR with a fix shortly.