proposition: Lemma irr_dom (E1: r ⊆ (⦗d⦘ ∪ ⦗d'⦘) ⨾ r ⨾ (⦗d⦘ ∪ ⦗d'⦘)) (E2: ⦗d⦘ ⨾ ⦗d'⦘ ⊆ ∅₂) (IRRd: irreflexive (⦗d⦘ ⨾ r ⨾ ⦗d⦘)) (IRRe: irreflexive (⦗d'⦘ ⨾ r ⨾ ⦗d'⦘)) : irreflexive r.
proof: Proof. rewrite step_dom; try edone. repeat rewrite irreflexive_union; splits; try done; generalize E2; basic_solver 8. Qed.
imports: HahnBase HahnSets HahnRelationsBasic HahnEquational HahnRewrite Setoid