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Hint Resolve power_mult: arith.

(* Specifications: *)
Lemma a2x : forall (a : M) (x : nat), power (o' a a) x = power a (x + x).
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Lemma power_eucl :
forall (m : M) (b q r : nat),
power m (q * b + r) = o' (power (power m b) q) (power m r).