#[global]
Instance lt_compat : Proper (eq ==> eq ==> iff) Bool.lt.

(* Specifications: *)
Lemma lt_trichotomy : forall b1 b2, { b1 < b2 } + { b1 = b2 } + { b2 < b1 }.
Lemma lt_total : forall b1 b2, b1 < b2 \/ b1 = b2 \/ b2 < b1.
Lemma lt_le_incl : forall b1 b2, b1 < b2 -> b1 <= b2.
Lemma le_lteq_dec : forall b1 b2, b1 <= b2 -> { b1 < b2 } + { b1 = b2 }.
Lemma le_lteq : forall b1 b2, b1 <= b2 <-> b1 < b2 \/ b1 = b2.