Definition active_term_order_superset_dec: forall (t t': active_term), {active_term_order_superset t t'} + {~ active_term_order_superset t t'}.Definition lex : (active_term * term) -> (active_term * term) -> Prop :=
  lexprod active_term_order_superset term_order.

Lemma wf_lex : well_founded lex.