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 ∘ _Qp )

Detailed syntax breakdown

Step Hyp Ref Expression
0 ccp ⊢ Cp
1 ccpms ⊢ cplMetSp
2 cqpa ⊢ _Qp
3 1 2 ccom ⊢ ( cplMetSp ∘ _Qp )
4 0 3 wceq ⊢ Cp = ( cplMetSp ∘ _Qp )