Loogle!

Result

Found 27 declarations mentioning Bool.not, Decidable.decide, and Eq. Of these, 5 match your pattern(s).

• Nat.not_decide_mod_two_eq_one 📋 Init.Data.Nat.Bitwise.Lemmas
  (x : ℕ) : (!decide (x % 2 = 1)) = decide (x % 2 = 0)
• BitVec.msb_sdiv_eq_decide 📋 Init.Data.BitVec.Bitblast
  {w : ℕ} {x y : BitVec w} : (x.sdiv y).msb = (decide (0 < w) && (!x.msb && y.msb && decide (-y ≤ x)) || x.msb && !y.msb && decide (y ≤ -x) && !decide (y = 0#w) || x.msb && y.msb && decide (x = BitVec.intMin w) && decide (y = -1#w))
• Bool.eq_false_of_not_eq_true' 📋 Mathlib.Data.Bool.Basic
  {a : Bool} : (!decide (a = true)) = true → a = false
• Bool.eq_true_of_not_eq_false' 📋 Mathlib.Data.Bool.Basic
  {a : Bool} : (!decide (a = false)) = true → a = true
• Bool.not_eq_iff 📋 Mathlib.Data.Bool.Basic
  {a b : Bool} : (!decide (a = b)) = true ↔ a ≠ b

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