proposition: Lemma step_lift_iff x y : (rel_lift eqv r) (eqv x) (eqv y) <-> (eqv ⨾ r ⨾ eqv) x y.
proof: Proof. Proof using REFL SYM TRAN. u; split; induction 1; desf; eauto. { repeat eexists; try apply H; splits; eauto. } all: do 2 eexists; splits; try edone; ins; desf; eauto. Qed.
imports: HahnBase HahnSets HahnRelationsBasic Setoid HahnEquational