| /- |
| Copyright (c) 2023 Heather Macbeth. All rights reserved. |
| Released under Apache 2.0 license as described in the file LICENSE. |
| Authors: Heather Macbeth |
| -/ |
| import Library.Tactic.Rel.Attr |
| import Mathlib.Tactic.SolveByElim |
| import Mathlib.Tactic.GCongr.Core |
|
|
| /-! # Extension to the `rel` tactic for the relation `↔` |
|
|
| The Mathlib `rel` and `gcongr` tactics don't work for the relation `↔` because the congruence lemmas |
| for `∃`, `∀` and `→` can't be tagged `@[gcongr]`. (It is possible to write a suitable variant for |
| `∃` but apparently not for the others.) So this is a quick-and-dirty implementation in that |
| setting. |
| -/ |
|
|
|
|
| open Lean Elab Tactic |
| open Mathlib Tactic |
|
|
| syntax (name := IffRelSyntax) "iff_rel" " [" term,* "] " : tactic |
|
|
| elab_rules : tactic | `(tactic| iff_rel [$t,*]) => do |
| liftMetaTactic <| fun g => |
| let cfg : SolveByElim.Config := { backtracking := false, maxDepth := 50 } |
| SolveByElim.solveByElim.processSyntax |
| cfg true false t.getElems.toList [] #[mkIdent `iff_rules] [g] |
|
|
| -- not sure where to hang error message |
| -- | throwError "cannot prove this by 'substituting' the listed relationships" |
|
|
| macro_rules | `(tactic| rel [$t,*]) => `(tactic| (repeat (intros |
|
|
| attribute [iff_rules] |
| Iff.refl |
| not_congr |
| and_congr_left and_congr_right and_congr |
| or_congr_left or_congr_right or_congr |
| imp_congr |
| iff_congr |
| exists_congr forall_congr' |
|
|
