Library Coq.PArith.POrderedType
Require Import BinPos Equalities Orders OrdersTac.
Local Open Scope positive_scope.
Module Positive_as_DT <: UsualDecidableTypeFull := Pos.
Note that the last module fulfills by subtyping many other
interfaces, such as DecidableType or EqualityType.
OrderedType structure for positive numbers
Module Positive_as_OT <: OrderedTypeFull := Pos.
Note that Positive_as_OT can also be seen as a UsualOrderedType
and a OrderedType (and also as a DecidableType).
An order tactic for positive numbers
Module PositiveOrder := OTF_to_OrderTac Positive_as_OT.
Ltac p_order := PositiveOrder.order.
Note that p_order is domain-agnostic: it will not prove
1<=2 or x<=x+x, but rather things like x<=y -> y<=x -> x=y.