Loogle!

Result

Found 7 declarations mentioning HMul.hMul, Equiv, Prod, and Fin.

• finProdFinEquiv 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} : Fin m × Fin n ≃ Fin (m * n)
• Nat.divModEquiv_symm_apply 📋 Mathlib.Logic.Equiv.Fin.Basic
  (n : ℕ) [NeZero n] (p : ℕ × Fin n) : n.divModEquiv.symm p = p.1 * n + ↑p.2
• Int.divModEquiv_symm_apply 📋 Mathlib.Logic.Equiv.Fin.Basic
  (n : ℕ) [NeZero n] (p : ℤ × Fin n) : (Int.divModEquiv n).symm p = p.1 * ↑n + ↑↑p.2
• finProdFinEquiv_apply_val 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} (x : Fin m × Fin n) : ↑(finProdFinEquiv x) = ↑x.2 + n * ↑x.1
• finProdFinEquiv_symm_apply 📋 Mathlib.Logic.Equiv.Fin.Basic
  {m n : ℕ} (x : Fin (m * n)) : finProdFinEquiv.symm x = (x.divNat, x.modNat)
• Matrix.toLin_finTwoProd_apply 📋 Mathlib.LinearAlgebra.Matrix.ToLin
  {R : Type u_1} [CommSemiring R] (a b c d : R) (x : R × R) : ((Matrix.toLin (Basis.finTwoProd R) (Basis.finTwoProd R)) !![a, b; c, d]) x = (a * x.1 + b * x.2, c * x.1 + d * x.2)
• Equiv.Perm.decomposeFin.symm_sign 📋 Mathlib.GroupTheory.Perm.Fin
  {n : ℕ} (p : Fin (n + 1)) (e : Equiv.Perm (Fin n)) : Equiv.Perm.sign (Equiv.Perm.decomposeFin.symm (p, e)) = (if p = 0 then 1 else -1) * Equiv.Perm.sign e

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 2c2d6a2 serving mathlib revision 7bcdce9