| /- |
| Copyright (c) 2023 Heather Macbeth. All rights reserved. |
| Released under Apache 2.0 license as described in the file LICENSE. |
| Authors: Heather Macbeth |
| -/ |
| import Mathlib.Tactic.Abel |
| import Mathlib.Tactic.Linarith |
| import Mathlib.Tactic.NormNum |
|
|
| /-! # Addarith tactic |
|
|
| The tactic `addarith` proves certain linear (in)equality goals over a commutative linear ordered |
| ring, by combining a specified set of linear (in)equality hypotheses. |
|
|
| This tactic is a deliberately weakened version of the Mathlib tactic `linarith`. |
| -/ |
|
|
| open Lean Elab Tactic |
| open Parser Tactic Syntax |
|
|
| syntax (name := addarith) "addarith" (" [" term,* "]")? : tactic |
|
|
| open Elab.Tactic Parser.Tactic |
| open Mathlib Tactic Abel |
|
|
| def addarithDischarger : TacticM Unit := do |
| try evalTactic (← `(tactic| simp (config := { decide := false }) only [one_mul, neg_mul])) catch _ => pure () |
| abelNFTarget {} |
| try evalTactic (← `(tactic| push_cast (config := { decide := false }) [zsmul_eq_mul])) catch _ => pure () |
| try evalTactic (← `(tactic| norm_num1)) catch _ => pure () |
|
|
| /-- |
| `addarith` attempts to use specified linear (in)equality hypotheses to prove a linear (in)equality |
| goal. It can add and subtract terms from both sides of hypotheses, add them together or subtract |
| them, and compare numerals. It cannot rescale hypotheses (i.e., multiply through by a factor). |
|
|
| An example: |
| ```lean |
| example {a b : ℤ} (h : a = 10 - b) : a + b ≤ 12 := by addarith [h] |
| ``` |
| -/ |
| elab_rules : tactic | `(tactic| addarith $[[$args,*]]?) => withMainContext do |
| (liftMetaFinishingTactic <| |
| Linarith.linarith true |
| (← ((args.map (TSepArray.getElems)).getD {}).mapM (elabTerm ·.raw none)).toList |
| { discharger := addarithDischarger }) |
| <|> throwError "addarith failed to prove this" |
|
|
| -- while we're at it, this turns off the succeed-with-noise behaviour of `ring_nf` with `ring` |
| macro_rules | `(tactic| ring) => `(tactic| ring_nf) |
|
|
