Loogle!

Result

Found 8 declarations mentioning Eq.rec, Iff, and HEq. Of these, 8 match your pattern(s).

• eqRec_heq_iff 📋 Init.Core
  {α : Sort u} {a : α} {motive : (b : α) → a = b → Sort v} {b : α} {refl : motive a ⋯} {h : a = b} {c : motive b h} : h ▸ refl ≍ c ↔ refl ≍ c
• heq_eqRec_iff 📋 Init.Core
  {α : Sort u} {a : α} {motive : (b : α) → a = b → Sort v} {b : α} {refl : motive a ⋯} {h : a = b} {c : motive b h} : c ≍ h ▸ refl ↔ c ≍ refl
• eqRec_heq_iff_heq 📋 Batteries.Logic
  {α : Sort u_1} {a : α} {motive : (a' : α) → a = a' → Sort u_2} {x : motive a ⋯} {a' : α} {e : a = a'} {β : Sort u_2} {y : β} : e ▸ x ≍ y ↔ x ≍ y
• heq_eqRec_iff_heq 📋 Batteries.Logic
  {α : Sort u_1} {a : α} {motive : (a' : α) → a = a' → Sort u_2} {x : motive a ⋯} {a' : α} {e : a = a'} {β : Sort u_2} {y : β} : y ≍ e ▸ x ↔ y ≍ x
• heq_rec_iff_heq 📋 Mathlib.Logic.Basic
  {α : Sort u_1} {a : α} {motive : (a' : α) → a = a' → Sort u_2} {x : motive a ⋯} {a' : α} {e : a = a'} {β : Sort u_2} {y : β} : y ≍ e ▸ x ↔ y ≍ x
• rec_heq_iff_heq 📋 Mathlib.Logic.Basic
  {α : Sort u_1} {a : α} {motive : (a' : α) → a = a' → Sort u_2} {x : motive a ⋯} {a' : α} {e : a = a'} {β : Sort u_2} {y : β} : e ▸ x ≍ y ↔ x ≍ y
• Fin.heq_fun_iff 📋 Mathlib.Data.Fin.Basic
  {α : Sort u_1} {k l : ℕ} (h : k = l) {f : Fin k → α} {g : Fin l → α} : f ≍ g ↔ ∀ (i : Fin k), f i = g ⟨↑i, ⋯⟩
• Fin.heq_fun₂_iff 📋 Mathlib.Data.Fin.Basic
  {α : Sort u_1} {k l k' l' : ℕ} (h : k = l) (h' : k' = l') {f : Fin k → Fin k' → α} {g : Fin l → Fin l' → α} : f ≍ g ↔ ∀ (i : Fin k) (j : Fin k'), f i j = g ⟨↑i, ⋯⟩ ⟨↑j, ⋯⟩

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 6ff4759 serving mathlib revision abad10c