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(**                     Order                        *)
Local Infix "<<" := ltb (at level 70, no associativity).
#[global]
Instance ltb_wd : Proper (N.eq ==> N.eq ==> Logic.eq) ltb.

(* Specifications: *)
Theorem ltb_base : forall n, 0 << n = if_zero false true n.
Theorem ltb_step :
forall m n, S m << n = recursion false (fun n' _ => m << n') n.