proposition: Lemma total_immediate_unique: forall A (r: A -> A -> Prop) (P: A -> Prop) (Tot: is_total P r) a b c (pa: P a) (pb: P b) (pc: P c) (iac: immediate r a c) (ibc: immediate r b c), a = b.
proof: Proof. ins; destruct (classic (a = b)) as [|N]; eauto. exfalso; unfold immediate in *; desf. eapply Tot in N; eauto; desf; eauto. Qed.
imports: Program.Basics Arith micromega.Lia Permutation List Setoid HahnBase HahnList HahnRelationsBasic HahnSets