TypeScript type equality and union types

equal.ts

// returns the intersection of all elements in the union T
// i.e. ToIntersect<T1 | T2 | .. | Tn> = T1 & T2 & .. & Tn
type ToIntersect<T> = (T extends unknown ? (x:T) => void : never) extends (x:infer U) => void ? U : never;

// check if T and U are equal
// Here, ([T] extends [U] ? _ : _) suppresses union distribution.
// See: https://github.com/microsoft/TypeScript/issues/29368
type Eq<T,U> = [T] extends [U] ? [U] extends [T] ? true : false : false;

// check if all elements in the union LS are equal by using (T & U) = (T | U) iff T = U
type EqAll<LS> = Eq<ToIntersect<LS>, LS>

type X = EqAll<{a:"1"} | {a:"1"}> // true

type Y = EqAll<{a:"1"} | {a:"1", b:"2"}> // false

type Z = EqAll<{b:"2", a:"1"} | {a:"1", b:"2"}> // true

type W = EqAll<{a:"1"|"2"} | {a:"1"}> // false