Neat proof, I can do better, I can "prove" that 1=2...
Here it is:
Assume
a=b
Multiply both side by b and get
ab=b^2
Subtract from both sides a^2, you get:
ab-a^2=b^2-a^2, which is, when factoring:
a(b-a)=(b+a)(b-a)
Divide both sides by the common factor (b-a), and you get
a=b+a,
but since a=b, the last relation is
a=2a,
and when dividing both sides with a, you get
1=2
QED.
As for The platinum group metals, now the long term hedge should be selling short Rh at $1530 and buying Pd at $200, Pt seems "fairly" priced here at about twice Gold.