immutable-state-nolib.ts

type State = {
    numbers: Array<number>;
}

const initialState:State = {
    numbers: [1, 2, 3, 4, 5, 6]
};

const { numbers } = initialState;

// let's print the initial state
console.log('initial state', initialState);

// now, i want to retrieve a new state with only even numbers
const newState = {
    ...state,
    numbers: numbers.filter((num:number):boolean => {
        return num % 2 === 0;
    })
}

// and let's print the new state 
console.log('new state', newState);

immutable-state-with-immutable.ts

import { Record } from "immutable";

type StateParams = {
    numbers: Array<number>;
}

const defaultValues:StateParams = {
    numbers: []
}

// https://facebook.github.io/immutable-js/docs/#/Record
class State extends Record(defaultValues) {
    numbers: Array<number>;

    constructor(params: StateParams) {
        super(params);
    }
}

const initialState:State = new State(<StateParams>{
    numbers: [1, 2, 3, 4, 5, 6]
})

const { numbers } = initialState;

// let's print the initial state
console.log('initial state', initialState);

// now, i want to retrieve a new state with only even numbers
const newState = initialState.set('numbers', numbers.filter((num:number):boolean => {
    return num % 2 === 0;
}));

console.log('new state', newState);

You forgot cast types:

const newState: State = initialState.set('numbers', numbers.filter((num:number):boolean => {
    return num % 2 === 0;
})) as State;

Otherwise Typescript compiler produces error