Theoreme Enumeration by subsection

[iustifico]

I am using "book (KOMA-script)" as documentclass and I want to enumerate my 
propositions, definitions etc. by subsection, like this:

I. Section
    I.1 Subsection
        Definition I.1.1
        Proposition I.1.2
    I.2 Subsection
        Proposition I.2.1
        Definition I.2.2
II Section
    II.1 Subsection
        Definition II.1.1
        Proposition II.1.2
    I.2 Subsection
        Proposition II.2.1
        Definition II.2.2

Second one: How do I change the style. At the moment lyx enumerates the 
definitions and propositions by section. That is not what I need...

Is this possible? If yes, how do I tell lyx, to do so? Thank you for your help.
Kind regards,
iustifico