Metamath Proof Explorer


Theorem hlimseqi

Description: A sequence with a limit on a Hilbert space is a sequence. (Contributed by NM, 16-Aug-1999) (New usage is discouraged.)

Ref Expression
Hypothesis hlim.1 A V
Assertion hlimseqi F v A F :

Proof

Step Hyp Ref Expression
1 hlim.1 A V
2 1 hlimi F v A F : A x + y z y norm F z - A < x
3 2 simplbi F v A F : A
4 3 simpld F v A F :