loogle-search

To search for Mathlib lemmas by type signature, you can query using functional shape patterns with wildcards (`_`) and type variables (`?a`) to find theorems when their names are unknown.

Type-directed theorem search is finding mathematical lemmas by matching their type signature shape rather than their name, which supports proof automation and exploration in formal verification environments.

You can find a Lean lemma transforming lists by searching the pattern `(?a → ?b) → List ?a → List ?b`, which returns matching functions like `List.map` from the Mathlib library.

Yes, you need a local or server-based Loogle index to efficiently query the Mathlib library and retrieve lemmas matching your specified type signature patterns.

Yes, you can use wildcards (`_`) and type variables (`?a`) when searching for theorems in Mathlib to perform flexible pattern matching against type signatures.

The best way to discover unknown lemmas in a Lean proof is type signature search, which matches the functional shape of the transformation you need, such as querying `Nontrivial _ ↔ _`.