Overriden class member annotated with a subtype could be a recipe for disaster (by design.. ;) )

TypeScript Version:
1.9.0-dev.20160505 with both strictNullChecks and noImplicitAny enabled.

Code:

class Animal {
    name: string = "Any animal";
}

class Dog extends Animal {
    name: string = "Dog";

    bark() {
        console.log("bark");
    }
}

class AnimalCage {
    member: Animal = new Animal();
}

class DogCage extends AnimalCage {
    member: Dog;
}

let dogCage = new DogCage();

if (dogCage.member != null) { // Yup, it is even checked for null or undefined, 
                              // but it turned out that wasn't enough..
    dogCage.member.bark(); // Bang!
}

Expected behavior:
Design a language where inheritance actually works.
(Edit: I was felling very 'passionate' when I wrote this.. sorry :) nothing personal)

Actual behavior:
By design:

    dogCage.member.bark();
                   ^

TypeError: dogCage.member.bark is not a function
    at Object.<anonymous> (C:\X\Documents\Drafts\TypeScript\Code\a.js:38:20)
    at Module._compile (module.js:541:32)
    at Object.Module._extensions..js (module.js:550:10)
    at Module.load (module.js:456:32)
    at tryModuleLoad (module.js:415:12)
    at Function.Module._load (module.js:407:3)
    at Function.Module.runMain (module.js:575:10)
    at startup (node.js:159:18)
    at node.js:444:3

Resolution:
tslint volunteers, for the rescue!

まず、issue にある TypeScript の例をコンパイルして実行し、その後、意図された継承の動作についての議論を読んでください。実現可能な貢献には、合意された言語設計、実装計画、および結果として得られる動作を示すリグレッションカバレッジが必要です。