The Coq Proof Assistant

# Library Coq.micromega.Lqa

Require Import QMicromega.
Require Import QArith.
Require Import RingMicromega.
Require Import VarMap.
Require Import DeclConstant.
Require Coq.micromega.Tauto.
Ltac rchange :=
let __wit := fresh "__wit" in
let __varmap := fresh "__varmap" in
let __ff := fresh "__ff" in
intros __wit __varmap __ff ;
change (Tauto.eval_bf (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
apply (QTautoChecker_sound __ff __wit).
Ltac rchecker_no_abstract := rchange ; vm_compute ; reflexivity.
Ltac rchecker_abstract := rchange ; vm_cast_no_check (eq_refl true).
Ltac rchecker := rchecker_no_abstract.
Here, lra stands for linear rational arithmetic
Ltac lra := xlra_Q rchecker.
Here, nra stands for non-linear rational arithmetic
Ltac nra := xnra_Q rchecker.
Ltac xpsatz dom d :=
let tac := lazymatch dom with
| Q =>
((xsos_Q rchecker) || (xpsatz_Q d rchecker))
| _ => fail "Unsupported domain"
end in tac.
Tactic Notation "psatz" constr(dom) int_or_var(n) := xpsatz dom n.
Tactic Notation "psatz" constr(dom) := xpsatz dom ltac:(-1).