Section proofs.
Hypothesis RDC_K : RelDec_Correct RD_K.
Hypothesis Refl : Reflexive R.
Hypothesis Sym : Symmetric R.
Hypothesis Trans : Transitive R.
Definition mapsto_alist (m : alist) k v : Prop :=
alist_find k m = Some v.

Lemma mapsto_alist_cons : forall k v m k' v',
mapsto_alist ((k',v') :: m) k v <->
(   (mapsto_alist m k v /\ ~R k k')
\/ (R k k' /\ v = v')).