Loogle!

Result

Found 3 declarations mentioning List.get and GetElem.getElem.

• List.get_eq_getElem 📋 Init.Data.List.Lemmas
  {α : Type u_1} {l : List α} {i : Fin l.length} : l.get i = l[↑i]
• Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.DerivedLitsInvariant.eq_1 📋 Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult
  {n : ℕ} (f : Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula n) (fassignments_size : f.assignments.size = n) (assignments : Array Std.Tactic.BVDecide.LRAT.Internal.Assignment) (assignments_size : assignments.size = n) (derivedLits : Std.Sat.CNF.Clause (Std.Tactic.BVDecide.LRAT.Internal.PosFin n)) : f.DerivedLitsInvariant fassignments_size assignments assignments_size derivedLits = ∀ (i : Fin n), have i_lt_assignments_size := ⋯; have i_lt_f_assignments_size := ⋯; have assignments_i := assignments[↑i]; have fassignments_i := f.assignments[↑i]; (assignments_i = fassignments_i ∧ ∀ l ∈ derivedLits, ↑l.1 ≠ ↑i) ∨ (∃ j, ↑(List.get derivedLits j).1 = ↑i ∧ assignments_i = Std.Tactic.BVDecide.LRAT.Internal.Assignment.addAssignment (List.get derivedLits j).2 fassignments_i ∧ ¬Std.Tactic.BVDecide.LRAT.Internal.Assignment.hasAssignment (List.get derivedLits j).2 fassignments_i = true ∧ ∀ (k : Fin (List.length derivedLits)), k ≠ j → ↑(List.get derivedLits k).1 ≠ ↑i) ∨ ∃ j1 j2, ↑(List.get derivedLits j1).1 = ↑i ∧ ↑(List.get derivedLits j2).1 = ↑i ∧ (List.get derivedLits j1).2 = true ∧ (List.get derivedLits j2).2 = false ∧ assignments_i = Std.Tactic.BVDecide.LRAT.Internal.Assignment.both ∧ fassignments_i = Std.Tactic.BVDecide.LRAT.Internal.Assignment.unassigned ∧ ∀ (k : Fin (List.length derivedLits)), k ≠ j1 → k ≠ j2 → ↑(List.get derivedLits k).1 ≠ ↑i
• List.get_eq_getElem? 📋 Mathlib.Data.List.Basic
  {α : Type u} (l : List α) (i : Fin l.length) : l.get i = l[i]?.get ⋯

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 187ba29 serving mathlib revision f4dee01