theorem Array.sizeOf_lt_of_mem' [DecidableEq α] [SizeOf α] {as : Array α} (h : as.contains a) : sizeOf a < sizeOf as := by simp [Membership.mem, contains, any, Id.run, BEq.beq, anyM] at h let rec aux (j : Nat) : anyM.loop (m := Id) (fun b => pure <| decide (a = b)) as as.size (Nat.le_refl ..) j = true → sizeOf a < sizeOf as := by unfold anyM.loop intro h split at h · simp only [bind, decide_eq_true_eq, pure] at h; split at h next he => subst a; apply sizeOf_get next => have ih := aux (j+1) h; assumption · contradiction termination_by as.size - j apply aux 0 h