Metamath Proof Explorer


Theorem caufpm

Description: Inclusion of a Cauchy sequence, under our definition. (Contributed by NM, 7-Dec-2006) (Revised by Mario Carneiro, 24-Dec-2013)

Ref Expression
Assertion caufpm D∞MetXFCauDFX𝑝𝑚

Proof

Step Hyp Ref Expression
1 iscau D∞MetXFCauDFX𝑝𝑚x+yFy:yFyballDx
2 1 simprbda D∞MetXFCauDFX𝑝𝑚