Loogle searches of Lean and Mathlib definitions and theorems.
You may also want to try the CLI version, the VS
Code extension, the
integration or the Zulip bot.
Loogle finds definitions and lemmas in various ways:
finds all lemmas whose statement somehow mentions the sine function.
By lemma name substring:
finds all lemmas that have
"differ"somewhere in their lemma name.
_ * (_ ^ _)
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
(?a -> ?b) -> List ?a -> List ?b
List ?a -> (?a -> ?b) -> List ?b
By main conclusion:
|- tsum _ = _ * tsum _
finds all lemmas where the conclusion (the subexpression to the right of all
∀) 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 _
tsum_lt_tsumeven though the hypothesis
f i < g iis 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
Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
woould find all lemmas which mention the constants
"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 (
assigned independently in each filter.
#lucky button will directly send you to the
documentation of the first hit.
You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is currently provided by Joachim Breitner <firstname.lastname@example.org>.
This is Loogle revision
c31f480 serving mathlib revision