Formal models of low-level applications rely often on the distinction between executable layer and underlying hardware abstraction. This is also the case for the model of Pip, a separation kernel formalised and verified in Coq using a shallow embedding. DEC is a deeply embedded imperative typed language with primitive recursion and specified in terms of small-step semantics, which we developed in Coq as a reified counterpart of the shallow embedding used for Pip. In this paper, we introduce DEC and its semantics, we present its interpreter based on the type soundness proof and extracted to Haskell, we introduce a Hoare logic to reason about DEC code, and we use this logic to verify properties of Pip as a case study, comparing the new proofs with those based on the shallow embedding. Notably DEC can import shallow specifications as external functions, thus allowing for reuse of the abstract hardware model.