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 ) |
| 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 ) |