[oop] What is an example of the Liskov Substitution Principle?

This formulation of the LSP is way too strong:

If for each object o1 of type S there is an object o2 of type T such that for all programs P de?ned in terms of T, the behavior of P is unchanged when o1 is substituted for o2, then S is a subtype of T.

Which basically means that S is another, completely encapsulated implementation of the exact same thing as T. And I could be bold and decide that performance is part of the behavior of P...

So, basically, any use of late-binding violates the LSP. It's the whole point of OO to to obtain a different behavior when we substitute an object of one kind for one of another kind!

The formulation cited by wikipedia is better since the property depends on the context and does not necessarily include the whole behavior of the program.