TypeScript key of Partial<T> aren't found in T

Question

I made a quick playground, if you follow the link you should also see the errors, but here's the code:

const normalizeValue = (v: any): any => {
  if (v === 'true') return true;
  if (v === 'false') return false;
  if (!Number.isNaN(+v)) return +v;
  return v
};

interface defaults {
  a: number,
  b: boolean,
  c: string,
}

const normalizeOptions = <T extends defaults>(
  defaultOps: T,
  inputOps: Partial<T>
): T => {
  const INPUT = { ...inputOps };
  const NORMAL = {};

  Object.keys(defaultOps).forEach((k) => {
    if (k in INPUT) {
      NORMAL[k] = normalizeValue(INPUT[k]);
    } else {
      NORMAL[k] = defaultOps[k];
    }
  });

  return NORMAL;
};

Why a property of Partial isn't the same type as with it's source object and how can I solve this?