(* now we've gotten what we need from the concrete definition, make it opaque so it doesn't slow down searches in the future *)
Global Opaque extension_approximation_seq.
Opaque extension_approximation_seq.

Lemma Rle_R1_pow: forall (x:R) (m n:nat), 0 <= x <= 1 -> (m <= n)%nat ->
x^n <= x^m.