Section lb_mask_nat.
Let lb_mask_nat_1 l : ⟬ ⟦l⟧⟭  ⪯  l.
Let lb_mask_nat_2 l : l ⪯  ⟬ ⟦l⟧⟭  .
Fact lb_mask_nat l : ⟬ ⟦l⟧⟭ ≂ l.
Hint Resolve lb_mask_eq_binary_le binary_le_eq_lb_mask : core.
Fact binary_le_trans x y z : x ≲ y -> y ≲ z -> x ≲ z.
Fact lb_mask_equiv_equal l m : l ≂ m <-> ⟦l⟧ = ⟦m⟧.
Fact equal_lb_mask_equiv x y : x = y <-> ⟬ x⟭ ≂⟬ y⟭.
Local Notation lbeq := lb_mask_equiv (only parsing).
Add Parametric Morphism: (lb_nat) with signature (lbeq) ==> (eq) as lb_nat_eq.

Theorem binary_le_diophatine x y :
dio_expression x
-> dio_expression y
-> dio_rel (fun v => x v ≲ y v).