Loogle!
Result
Found 80 definitions mentioning HMul.hMul, tsum and Eq. Of these, 7 match your pattern(s).
- Summable.tsum_mul_left Mathlib.Topology.Algebra.InfiniteSum.Ring
∀ {ι : Type u_1} {α : Type u_4} [inst : NonUnitalNonAssocSemiring α] [inst_1 : TopologicalSpace α] [inst_2 : TopologicalSemiring α] {f : ι → α} [inst_3 : T2Space α] (a : α), Summable f → ∑' (i : ι), a * f i = a * ∑' (i : ι), f i - tsum_mul_left Mathlib.Topology.Algebra.InfiniteSum.Ring
∀ {ι : Type u_1} {α : Type u_4} [inst : DivisionSemiring α] [inst_1 : TopologicalSpace α] [inst_2 : TopologicalSemiring α] {f : ι → α} {a : α} [inst_3 : T2Space α], ∑' (x : ι), a * f x = a * ∑' (x : ι), f x - NNReal.tsum_mul_left Mathlib.Topology.Instances.NNReal
∀ {α : Type u_1} (a : NNReal) (f : α → NNReal), ∑' (x : α), a * f x = a * ∑' (x : α), f x - ENNReal.tsum_mul_left Mathlib.Topology.Instances.ENNReal
∀ {α : Type u_1} {a : ENNReal} {f : α → ENNReal}, ∑' (i : α), a * f i = a * ∑' (i : α), f i - Real.tsum_exp_neg_mul_int_sq Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation
∀ {a : ℝ}, 0 < a → ∑' (n : ℤ), Real.exp (-Real.pi * a * ↑n ^ 2) = 1 / a ^ (1 / 2) * ∑' (n : ℤ), Real.exp (-Real.pi / a * ↑n ^ 2) - Complex.tsum_exp_neg_mul_int_sq Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation
∀ {a : ℂ}, 0 < a.re → ∑' (n : ℤ), Complex.exp (-↑Real.pi * a * ↑n ^ 2) = 1 / a ^ (1 / 2) * ∑' (n : ℤ), Complex.exp (-↑Real.pi / a * ↑n ^ 2) - Complex.tsum_exp_neg_quadratic Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation
∀ {a : ℂ}, 0 < a.re → ∀ (b : ℂ), ∑' (n : ℤ), Complex.exp (-↑Real.pi * a * ↑n ^ 2 + 2 * ↑Real.pi * b * ↑n) = 1 / a ^ (1 / 2) * ∑' (n : ℤ), Complex.exp (-↑Real.pi / a * (↑n + Complex.I * b) ^ 2)
About
Loogle searches Lean and Mathlib definitions and theorems.
You can use Loogle from witin the Lean4 VSCode language extension
using (by default) Ctrl-K Ctrl-S. You can also try 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:
By constant:
🔍Real.sin
finds all lemmas whose statement somehow mentions the sine function.By lemma name substring:
🔍"differ"
finds all lemmas that have"differ"
somewhere in their lemma name.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
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 findtsum_lt_tsum
even though the hypothesisf 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, _ * _, _ ^ _, |- _ < _ → _
woould 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 f46663a
serving mathlib revision c78db14