Loogle!

Result

Found 11 declarations whose name contains "sql".

• Std.Time.Formats.sqlDate 📋 Std.Time.Format
  : Std.Time.GenericFormat Std.Time.Awareness.any
• Std.Time.PlainDate.toSQLDateString 📋 Std.Time.Format
  (input : Std.Time.PlainDate) : String
• Std.Time.PlainDate.fromSQLDateString 📋 Std.Time.Format
  (input : String) : Except String Std.Time.PlainDate
• Zsqrtd.SqLe 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  (a c b d : ℕ) : Prop
• Zsqrtd.sqLe_of_le 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  {c d x y z w : ℕ} (xz : z ≤ x) (yw : y ≤ w) (xy : Zsqrtd.SqLe x c y d) : Zsqrtd.SqLe z c w d
• Zsqrtd.sqLe_smul 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  {c d x y : ℕ} (n : ℕ) (xy : Zsqrtd.SqLe x c y d) : Zsqrtd.SqLe (n * x) c (n * y) d
• Zsqrtd.not_sqLe_succ 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  (c d y : ℕ) (h : 0 < c) : ¬Zsqrtd.SqLe (y + 1) c 0 d
• Zsqrtd.sqLe_add 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  {c d x y z w : ℕ} (xy : Zsqrtd.SqLe x c y d) (zw : Zsqrtd.SqLe z c w d) : Zsqrtd.SqLe (x + z) c (y + w) d
• Zsqrtd.sqLe_cancel 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  {c d x y z w : ℕ} (zw : Zsqrtd.SqLe y d x c) (h : Zsqrtd.SqLe (x + z) c (y + w) d) : Zsqrtd.SqLe z c w d
• Zsqrtd.sqLe_add_mixed 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  {c d x y z w : ℕ} (xy : Zsqrtd.SqLe x c y d) (zw : Zsqrtd.SqLe z c w d) : c * (x * z) ≤ d * (y * w)
• Zsqrtd.sqLe_mul 📋 Mathlib.NumberTheory.Zsqrtd.Basic
  {d x y z w : ℕ} : (Zsqrtd.SqLe x 1 y d → Zsqrtd.SqLe z 1 w d → Zsqrtd.SqLe (x * w + y * z) d (x * z + d * y * w) 1) ∧ (Zsqrtd.SqLe x 1 y d → Zsqrtd.SqLe w d z 1 → Zsqrtd.SqLe (x * z + d * y * w) 1 (x * w + y * z) d) ∧ (Zsqrtd.SqLe y d x 1 → Zsqrtd.SqLe z 1 w d → Zsqrtd.SqLe (x * z + d * y * w) 1 (x * w + y * z) d) ∧ (Zsqrtd.SqLe y d x 1 → Zsqrtd.SqLe w d z 1 → Zsqrtd.SqLe (x * w + y * z) d (x * z + d * y * w) 1)

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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 8e80836 serving mathlib revision 6ef8cc2