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How to get an optimal simplification?


I expected to get:

with the expression:
  Simplify[{a - b, b - c, c - a}, {t1 == a - b, t2 == b - c, t3 == c -

But I only get {-t2-t3,t2,t3}, which is a little bit annoying.

I know I can do the simplifications separately like,
  Simplify[Simplify[Simplify[{a - b, b - c, c - a}, t1 == a - b], t2
== b - c], t3 == c - a]

But I still like to get the optimal result with one simplify

Is there an answer? (the answer is useful for one of my big


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