Notations and Opinions

[GFR]

As a derivation:
b[r]\ x = b[r]<-1> x and
x /[r]n = ([r]n)<-1>(x)

Though I think the mind has somewhat to cope with the last line in daily calculation.

I would better put the last line as:
x /[r]n = x [r]n<-1>

Keeping in mind the fact that the operators act from the left and from the right, respectively and that their operaional environment is not commutative. In particular, I am supposing the following equality among operators:
/[r]n = [r]n<-1> = ([r]n)^(-1).

GFR