[Typescript Challenges] 10. Medium Include

Implement the JavaScript Array.includes function in the type system. A type takes the two arguments. The output should be a boolean true or false.

For example:

type isPillarMen = Includes<['Kars', 'Esidisi', 'Wamuu', 'Santana'], 'Dio'> // expected to be `false`

/* _____________ Your Code Here _____________ */
type IsEqual<T, U> =
	(<V>(x: V) => V extends T ? 1 : 2) extends
	(<V>(x: V) => V extends U ? 1 : 2)
		? true
		: false;
    
type Includes<T extends readonly any[], U> =
  T extends [infer First, ...infer Rest]
    ? IsEqual<First, U> extends true ? true : Includes<Rest, U>
    : false;

/* _____________ Test Cases _____________ */
import type { Equal, Expect } from '@type-challenges/utils'

type cases = [
  Expect<Equal<Includes<['Kars', 'Esidisi', 'Wamuu', 'Santana'], 'Kars'>, true>>,
  Expect<Equal<Includes<['Kars', 'Esidisi', 'Wamuu', 'Santana'], 'Dio'>, false>>,
  Expect<Equal<Includes<[1, 2, 3, 5, 6, 7], 7>, true>>,
  Expect<Equal<Includes<[1, 2, 3, 5, 6, 7], 4>, false>>,
  Expect<Equal<Includes<[1, 2, 3], 2>, true>>,
  Expect<Equal<Includes<[1, 2, 3], 1>, true>>,
  Expect<Equal<Includes<[{}], { a: 'A' }>, false>>,
  Expect<Equal<Includes<[boolean, 2, 3, 5, 6, 7], false>, false>>,
  Expect<Equal<Includes<[true, 2, 3, 5, 6, 7], boolean>, false>>,
  Expect<Equal<Includes<[false, 2, 3, 5, 6, 7], false>, true>>,
  Expect<Equal<Includes<[{ a: 'A' }], { readonly a: 'A' }>, false>>,
  Expect<Equal<Includes<[{ readonly a: 'A' }], { a: 'A' }>, false>>,
  Expect<Equal<Includes<[1], 1 | 2>, false>>,
  Expect<Equal<Includes<[1 | 2], 1>, false>>,
  Expect<Equal<Includes<[null], undefined>, false>>,
  Expect<Equal<Includes<[undefined], null>, false>>,
]