aChild is a superset of aParent's abilities.
class Fox : Animal
Because each Fox is an Animal. But the other way is not always true (not every Animal is a Fox).
Also it seems that you have your OOP mixed up. This is not a Parent-Child relationship, because there's no composition/trees involved. This is a Ancestor/Descendant inheritance relation.
Inheritance is "type of" not "contains". Hence it's Fox is a type of Animal, in your case it doesn't sound right -- "Child is a type of Parent" ?
class Animal {}
class Fox : Animal {}
class Fish : Animal {}
Animal a = new Fox(); // ok!
Animal b = new Fish(); // ok!
Fox f = b; // obviously no!
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