Library Stdlib.micromega.Psatz

Require Import ZMicromega.
Require Import QMicromega.
Require Import RMicromega.
Require Import QArith.
Require Import ZArith.
Require Import Rdefinitions.
Require Import RingMicromega.
Require Import VarMap.
Require Stdlib.micromega.Tauto.
Require Lia.
Require Lra.
Require Lqa.


Ltac lia := Lia.lia.

Ltac nia := Lia.nia.

Ltac xpsatz dom d :=
  let tac := lazymatch dom with
  | Z => (xsos_Z Lia.zchecker) || (xpsatz_Z d Lia.zchecker)
  | R => (xsos_R Lra.rchecker) || (xpsatz_R d Lra.rchecker)
  | Q => (xsos_Q Lqa.rchecker) || (xpsatz_Q d Lqa.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).

Ltac psatzl dom :=
  let tac := lazymatch dom with
  | Z => Lia.lia
  | Q => Lqa.lra
  | R => Lra.lra
  | _ => fail "Unsupported domain"
  end in tac.

Ltac lra :=
  first [ psatzl R | psatzl Q ].

Ltac nra :=
  first [ Lra.nra | Lqa.nra ].