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.

Theorem remove_neq_alist:
forall (m : alist) (k k' : K), ~R k' k -> alist_find k (alist_remove k' m) = alist_find k m.