Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.Numbers.Integer.Binary.ZBinary

Require Import ZAxioms ZProperties BinInt.
Local Open Scope Z_scope.
BinInt.Z is already implementing ZAxiomsMiniSig
Module Z
<: ZAxiomsSig <: UsualOrderedTypeFull <: TotalOrder
<: UsualDecidableTypeFull
:= BinInt.Z.

# An order tactic for integers

Ltac z_order := Z.order.
Note that z_order is domain-agnostic: it will not prove 1<=2 or x<=x+x, but rather things like x<=y -> y<=x -> x=y.
Section TestOrder.
Let test : forall x y, x<=y -> y<=x -> x=y.
End TestOrder.
Z forms a ring