226a90f1eb
This PR adds `+grind` and `+try?` options to `exact?` and `apply?`
tactics.
## `+grind` option
When `+grind` is enabled, `grind` is used as a fallback discharger for
subgoals that `solve_by_elim` cannot close. The proof is wrapped in
`Grind.Marker` so suggestions display `(by grind)` instead of the
complex grind proof term.
Example:
```lean
axiom foo (x : Nat) : x < 37 → 5 < x → x.log2 < 6
/--
info: Try this:
[apply] exact foo x (by grind) (by grind)
-/
#guard_msgs in
example (x : Nat) (h₁ : x < 30) (h₂ : 8 < x) : x.log2 < 6 := by
exact? +grind
```
## `+try?` option
When `+try?` is enabled, `try?` is used as a fallback discharger for
subgoals. This is useful when subgoals require induction or other
strategies that `try?` can find but `solve_by_elim` and `grind` cannot.
Example:
```lean
inductive MyList (α : Type _) where
| nil : MyList α
| cons : α → MyList α → MyList α
axiom MyListProp : MyList α → Prop
@[grind .] axiom mylist_nil : MyListProp (MyList.nil : MyList α)
@[grind .] axiom mylist_cons : ∀ (x : α) (xs : MyList α), MyListProp xs → MyListProp (MyList.cons x xs)
axiom qux (xs : MyList α) (p : MyListProp xs) : MyListProp2 xs
/--
info: Try this:
[apply] exact qux xs (by try?)
-/
example (xs : MyList α) : MyListProp2 xs := by
exact? +try?
```
🤖 Prepared with Claude Code
---------
Co-authored-by: Claude <noreply@anthropic.com>
79 lines
3.9 KiB
Text
79 lines
3.9 KiB
Text
-- This tests the `#info_trees in` command.
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-- If it proves too fragile to test the result using `#guard_msgs`,
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-- it is fine to simply remove the `#guard_msgs` and expected output.
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/--
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info: • [Command] @ ⟨79, 0⟩-⟨79, 40⟩ @ Lean.Elab.Command.elabDeclaration
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• [Term] Nat : Type @ ⟨79, 15⟩-⟨79, 18⟩ @ Lean.Elab.Term.elabIdent
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• [Completion-Id] Nat : some Sort.{?_uniq.1} @ ⟨79, 15⟩-⟨79, 18⟩
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• [Term] Nat : Type @ ⟨79, 15⟩-⟨79, 18⟩
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• [Term] n (isBinder := true) : Nat @ ⟨79, 11⟩-⟨79, 12⟩
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• [Term] 0 ≤ n : Prop @ ⟨79, 22⟩-⟨79, 27⟩ @ «_aux_Init_Notation___macroRules_term_≤__2»
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• [MacroExpansion]
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0 ≤ n
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===>
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binrel% LE.le✝ 0 n
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• [Term] 0 ≤ n : Prop @ ⟨79, 22⟩†-⟨79, 27⟩† @ Lean.Elab.Term.Op.elabBinRel
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• [Term] 0 ≤ n : Prop @ ⟨79, 22⟩†-⟨79, 27⟩†
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• [Completion-Id] LE.le✝ : none @ ⟨79, 22⟩†-⟨79, 27⟩†
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• [Term] 0 : Nat @ ⟨79, 22⟩-⟨79, 23⟩ @ Lean.Elab.Term.elabNumLit
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• [Term] n : Nat @ ⟨79, 26⟩-⟨79, 27⟩ @ Lean.Elab.Term.elabIdent
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• [Completion-Id] n : none @ ⟨79, 26⟩-⟨79, 27⟩
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• [Term] n : Nat @ ⟨79, 26⟩-⟨79, 27⟩
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• [CustomInfo(Lean.Elab.Term.AsyncBodyInfo)]
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• [Term] n (isBinder := true) : Nat @ ⟨79, 11⟩-⟨79, 12⟩
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• [CustomInfo(Lean.Elab.Term.BodyInfo)]
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• [Tactic] @ ⟨79, 31⟩-⟨79, 40⟩
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(Term.byTactic
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"by"
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(Tactic.tacticSeq (Tactic.tacticSeq1Indented [(Tactic.exact? "exact?" (Tactic.optConfig []) [])])))
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before ⏎
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n : Nat
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⊢ 0 ≤ n
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after no goals
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• [Tactic] @ ⟨79, 31⟩-⟨79, 33⟩
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"by"
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before ⏎
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n : Nat
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⊢ 0 ≤ n
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after no goals
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• [Tactic] @ ⟨79, 34⟩-⟨79, 40⟩ @ Lean.Elab.Tactic.evalTacticSeq
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(Tactic.tacticSeq (Tactic.tacticSeq1Indented [(Tactic.exact? "exact?" (Tactic.optConfig []) [])]))
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before ⏎
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n : Nat
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⊢ 0 ≤ n
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after no goals
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• [Tactic] @ ⟨79, 34⟩-⟨79, 40⟩ @ Lean.Elab.Tactic.evalTacticSeq1Indented
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(Tactic.tacticSeq1Indented [(Tactic.exact? "exact?" (Tactic.optConfig []) [])])
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before ⏎
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n : Nat
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⊢ 0 ≤ n
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after no goals
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• [Tactic] @ ⟨79, 34⟩-⟨79, 40⟩ @ Lean.Elab.LibrarySearch.evalExact
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(Tactic.exact? "exact?" (Tactic.optConfig []) [])
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before ⏎
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n : Nat
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⊢ 0 ≤ n
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after no goals
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• [Tactic] @ ⟨79, 34⟩†-⟨79, 40⟩† @ Lean.Elab.Tactic.evalExact
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(Tactic.exact "exact" (Term.app `Nat.zero_le [`n]))
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before ⏎
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n : Nat
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⊢ 0 ≤ n
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after no goals
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• [Term] Nat.zero_le n : 0 ≤ n @ ⟨1, 1⟩†-⟨1, 1⟩† @ Lean.Elab.Term.elabApp
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• [Completion-Id] Nat.zero_le : some LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) _uniq.37 @ ⟨1, 0⟩†-⟨1, 0⟩†
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• [Term] Nat.zero_le : ∀ (n : Nat), 0 ≤ n @ ⟨1, 0⟩†-⟨1, 0⟩†
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• [Term] n : Nat @ ⟨1, 5⟩†-⟨1, 5⟩† @ Lean.Elab.Term.elabIdent
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• [Completion-Id] n : some Nat @ ⟨1, 5⟩†-⟨1, 5⟩†
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• [Term] n : Nat @ ⟨1, 5⟩†-⟨1, 5⟩†
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• [CustomInfo(Lean.Meta.Tactic.TryThis.TryThisInfo)]
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• [Term] t (isBinder := true) : ∀ (n : Nat), 0 ≤ n @ ⟨79, 8⟩-⟨79, 9⟩
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• [Term] t (isBinder := true) : ∀ (n : Nat), 0 ≤ n @ ⟨79, 8⟩-⟨79, 9⟩
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---
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info: Try this:
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[apply] exact Nat.zero_le n
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-/
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#guard_msgs in
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#info_trees in
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theorem t (n : Nat) : 0 ≤ n := by exact?
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