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 mapsto_remove_eq_alist : forall (m : list (K * V)) (k : K) (v : V),
~mapsto_alist (remove k m) k v.