(* 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 extension_approximation_seq_cauchy_aux:
forall (m n:nat) (x:point_set X),
Rabs (proj1_sig (extension_approximation_seq m) x -
proj1_sig (extension_approximation_seq n) x) <=
Rabs ((2/3)^m - (2/3)^n).