Loogle!

Result

Found 4 declarations mentioning Invertible.map.

• Invertible.map 📋 Mathlib.Algebra.Group.Invertible.Basic
  {R : Type u_1} {S : Type u_2} {F : Type u_3} [MulOneClass R] [MulOneClass S] [FunLike F R S] [MonoidHomClass F R S] (f : F) (r : R) [Invertible r] : Invertible (f r)
• Invertible.ofLeftInverse_invOf 📋 Mathlib.Algebra.Group.Invertible.Basic
  {R : Type u_1} {S : Type u_2} {G : Type u_3} [MulOneClass R] [MulOneClass S] [FunLike G S R] [MonoidHomClass G S R] (f : R → S) (g : G) (r : R) (h : Function.LeftInverse (⇑g) f) [Invertible (f r)] : ⅟ r = ⅟ (g (f r))
• invertibleEquivOfLeftInverse_symm_apply 📋 Mathlib.Algebra.Group.Invertible.Basic
  {R : Type u_1} {S : Type u_2} {F : Type u_3} {G : Type u_4} [Monoid R] [Monoid S] [FunLike F R S] [MonoidHomClass F R S] [FunLike G S R] [MonoidHomClass G S R] (f : F) (g : G) (r : R) (h : Function.LeftInverse ⇑g ⇑f) (x✝ : Invertible r) : (invertibleEquivOfLeftInverse f g r h).symm x✝ = Invertible.map f r
• ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf 📋 Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
  {R : Type u1} [CommRing R] (M : Type u2) [AddCommGroup M] [Module R M] (r : R) (x✝ : Invertible ((algebraMap R (ExteriorAlgebra R M)) r)) : ⅟ r = ⅟ (ExteriorAlgebra.algebraMapInv ((algebraMap R (ExteriorAlgebra R M)) r))

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 19971e9 serving mathlib revision 40fea08