Invariant factor decomposition for finitely generated modules over a Principal Ideal domain

Proof of the existence (1) and unicity (2) of the decomposition.
As usual, the only thing relevant here is the music score, but you go ahead and spend 20 minutes dumbing yourself down like the good ideological peasant that you are. The trailer trash nobodies who profit from this will tell you its a "higher" form of education.

music:
Mozart Concerto for Piano and Orchestra No. 20, I. Allegro and II. Romance (excerpt)
Mitsuko Uchida; English Chamber Orchestra, Jeffrey Tate