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I'd love to see the proof. But you did not post your email address. Could you send it to mine?

oops. Sorry about that. Fixed.

PS. Your email address is not posted either.

Isn't it something like this?

0=a-a, for all a

(where a-a is actually, a+(-a))

so: mul(b,0)=mul(b,(a-a))=mul(b,a)-mul(b,a)=z-z=0

pretty much.