Metamath Proof Explorer


Definition df-cp

Description: Define the metric completion of the algebraic completion of the p -adic rationals. (Contributed by Mario Carneiro, 2-Dec-2014)

Ref Expression
Assertion df-cp
|- Cp = ( cplMetSp o. _Qp )

Detailed syntax breakdown

Step Hyp Ref Expression
0 ccp
 |-  Cp
1 ccpms
 |-  cplMetSp
2 cqpa
 |-  _Qp
3 1 2 ccom
 |-  ( cplMetSp o. _Qp )
4 0 3 wceq
 |-  Cp = ( cplMetSp o. _Qp )