The Coq Proof Assistant

# Library Coq.micromega.Lia

Require Import ZMicromega.
Require Import ZArith.
Require Import RingMicromega.
Require Import VarMap.
Require Coq.micromega.Tauto.
Ltac preprocess :=
zify ; unfold Z.succ in * ; unfold Z.pred in *.
Ltac zchange :=
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit).
Ltac zchecker_no_abstract := zchange ; vm_compute ; reflexivity.
Ltac zchecker_abstract := zchange ; vm_cast_no_check (eq_refl true).
Ltac zchecker := zchecker_no_abstract.
Ltac lia := preprocess; xlia zchecker.
Ltac nia := preprocess; xnlia zchecker.