Loogle!

(LieAlgebra.Basis.A ∨ SSet.Subcomplex.Pairing.RankFunction.b) → ¬GenContFract.Pair.b → A

Error

Unknown identifier `A`

Did you maybe mean

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 3a988db serving mathlib revision bb88d2c