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include "sequence.ma".
-include "metric_lattice.ma". (* we should probably use something weaker *)
+include "metric_space.ma".
include "nat/orders.ma".
definition tends0 ≝
λO:pogroup.λs:sequence O.∀e:O.0 < e → ∃N.∀n.N < n → -e < s n ∧ s n < e.
definition d2s ≝
- λR.λml:mlattice R.λs:sequence ml.λk.λn. δ (s n) k.
+ λR.λms:metric_space R.λs:sequence ms.λk.λn. δ (s n) k.
notation "s ⇝ x" non associative with precedence 50 for @{'tends $s $x}.
interpretation "tends to" 'tends s x =