proposition: Lemma lforall_notin_vars_solved_eqn_2 : forall n u l' l, lforall (notin ((Var n, u) :: l')) l -> lforall (notin_vars_solved_eqn u) (map (solved_eqn_sub (single n u)) l).
proof: Proof. induction l; simpl. auto. destruct a. unfold notin_vars_solved_eqn at 1, notin_eqn, notin at 1. simpl. mem. split_all. Qed.
imports: Coq(Relations Wellfounded) CoLoR(ASubstitution ATerm EqUtil ListUtil LogicUtil VecUtil AVariables BoolUtil NatUtil SN AVariables Lexico)