proposition: Lemma acyclic_utt r r' (T: transitive r) (T': transitive r') : acyclic (r ∪ r') <-> irreflexive r /\ irreflexive r' /\ acyclic (r ⨾ r').
proof: Proof. ins; rewrite acyclic_ut, ct_of_trans, acyclic_rotl; ins. by unfold acyclic; rewrite ct_of_trans. Qed.
imports: Arith micromega.Lia HahnBase HahnList HahnRelationsBasic HahnEquational HahnMaxElt HahnRewrite HahnDom HahnMinPath HahnPath