proposition: Lemma In_KeyBasedPartition_snd : forall {TValue} k k' (m: t TValue), In k' (snd (partition (KeyBasedPartitioningFunction TValue k) m)) -> ~ E.eq k k'.
proof: Proof. intros * in_falses. apply In_MapsTo in in_falses. destruct in_falses as [ val ( maps_to' & _ ) ]. eapply MapsTo_KeyBasedPartition_snd; eauto. Qed.
imports: Coq.FSets.FMapInterface Coq.FSets.FMapFacts Coq.Program.Program Coq.Structures.OrderedTypeEx Fiat.Common Fiat.Common.SetEq Fiat.Common.SetEqProperties Fiat.Common.List.ListFacts Fiat.Common.List.ListMorphisms Fiat.Common.LogicFacts Fiat.Common.SetoidClassInstances