The Grothendieck group of completed distribution algebras

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Let G be a compact p-adic analytic group with no element of order p and H be its maximal uniform normal subgroup. Let K be a finite extention of Qₚ. We show that the Grothendieck group of the completion of the algebra of locally analytic distributions on G is isomorphic to Zᶜ where c is the number of conjugacy classes in G/H relative prime to p, provided that K is big enough. In addition we will see the algebra K[[G]] of continuous distributions on G has the same Grothendieck group.