Loogle!
Result
Found 17 definitions mentioning Finset and Infinite.
- instInfiniteFinset Mathlib.Data.Fintype.Card
∀ {α : Type u_1} [inst : Infinite α], Infinite (Finset α) - Infinite.exists_subset_card_eq Mathlib.Data.Fintype.Card
∀ (α : Type u_4) [inst : Infinite α] (n : ℕ), ∃ s, s.card = n - Infinite.exists_not_mem_finset Mathlib.Data.Fintype.Card
∀ {α : Type u_1} [inst : Infinite α] (s : Finset α), ∃ x, x ∉ s - Infinite.exists_superset_card_eq Mathlib.Data.Fintype.Card
∀ {α : Type u_1} [inst : Infinite α] (s : Finset α) (n : ℕ), s.card ≤ n → ∃ t, s ⊆ t ∧ t.card = n - Finset.exists_card_eq Mathlib.Data.Set.Finite
∀ {α : Type u} [inst : Infinite α] (n : ℕ), ∃ s, s.card = n - Finset.exists_not_mem Mathlib.Data.Set.Finite
∀ {α : Type u} [inst : Infinite α] (s : Finset α), ∃ a, a ∉ s - Cardinal.mk_finset_of_infinite Mathlib.SetTheory.Cardinal.Ordinal
∀ (α : Type u) [inst : Infinite α], Cardinal.mk (Finset α) = Cardinal.mk α - Cardinal.mk_compl_finset_of_infinite Mathlib.SetTheory.Cardinal.Ordinal
∀ {α : Type u_1} [inst : Infinite α] (s : Finset α), Cardinal.mk ↑(↑s)ᶜ = Cardinal.mk α - Cardinal.le_range_of_union_finset_eq_top Mathlib.SetTheory.Cardinal.Cofinality
∀ {α : Type u_2} {β : Type u_3} [inst : Infinite β] (f : α → Finset β), ⋃ a, ↑(f a) = ⊤ → Cardinal.mk β ≤ Cardinal.mk ↑(Set.range f) - SimpleGraph.componentCompl_nonempty_of_infinite Mathlib.Combinatorics.SimpleGraph.Ends.Defs
∀ {V : Type u} (G : SimpleGraph V) [inst : Infinite V] (K : Finset V), Nonempty (G.ComponentCompl ↑K) - SimpleGraph.compononentComplFunctor_nonempty_of_infinite Mathlib.Combinatorics.SimpleGraph.Ends.Properties
∀ {V : Type} (G : SimpleGraph V) [inst : Infinite V] (K : (Finset V)ᵒᵖ), Nonempty (G.componentComplFunctor.obj K) - SimpleGraph.nonempty_ends_of_infinite Mathlib.Combinatorics.SimpleGraph.Ends.Properties
∀ {V : Type} (G : SimpleGraph V) [inst : G.LocallyFinite] [inst : Fact G.Preconnected] [inst : Infinite V], G.end.Nonempty - ClassGroup.finsetApprox Mathlib.NumberTheory.ClassNumber.Finite
{R : Type u_1} → {S : Type u_2} → [inst : EuclideanDomain R] → [inst_1 : CommRing S] → [inst_2 : IsDomain S] → [inst_3 : Algebra R S] → {abv : AbsoluteValue R ℤ} → {ι : Type u_5} → [inst_4 : DecidableEq ι] → [inst_5 : Fintype ι] → Basis ι R S → abv.IsAdmissible → [inst : Infinite R] → [inst : DecidableEq R] → Finset R - ClassGroup.finsetApprox.zero_not_mem Mathlib.NumberTheory.ClassNumber.Finite
∀ {R : Type u_1} {S : Type u_2} [inst : EuclideanDomain R] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra R S] {abv : AbsoluteValue R ℤ} {ι : Type u_5} [inst_4 : DecidableEq ι] [inst_5 : Fintype ι] (bS : Basis ι R S) (adm : abv.IsAdmissible) [inst_6 : Infinite R] [inst_7 : DecidableEq R], 0 ∉ ClassGroup.finsetApprox bS adm - ClassGroup.mem_finsetApprox Mathlib.NumberTheory.ClassNumber.Finite
∀ {R : Type u_1} {S : Type u_2} [inst : EuclideanDomain R] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra R S] {abv : AbsoluteValue R ℤ} {ι : Type u_5} [inst_4 : DecidableEq ι] [inst_5 : Fintype ι] (bS : Basis ι R S) (adm : abv.IsAdmissible) [inst_6 : Infinite R] [inst_7 : DecidableEq R] {x : R}, x ∈ ClassGroup.finsetApprox bS adm ↔ ∃ i j, i ≠ j ∧ (ClassGroup.distinctElems bS adm) i - (ClassGroup.distinctElems bS adm) j = x - ClassGroup.exists_mem_finsetApprox Mathlib.NumberTheory.ClassNumber.Finite
∀ {R : Type u_1} {S : Type u_2} [inst : EuclideanDomain R] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra R S] {abv : AbsoluteValue R ℤ} {ι : Type u_5} [inst_4 : DecidableEq ι] [inst_5 : Fintype ι] (bS : Basis ι R S) (adm : abv.IsAdmissible) [inst_6 : Infinite R] [inst_7 : DecidableEq R] (a : S) {b : R}, b ≠ 0 → ∃ q, ∃ r ∈ ClassGroup.finsetApprox bS adm, abv ((Algebra.norm R) (r • a - b • q)) < abv ((Algebra.norm R) ((algebraMap R S) b)) - ClassGroup.exists_mem_finset_approx' Mathlib.NumberTheory.ClassNumber.Finite
∀ {R : Type u_1} {S : Type u_2} (L : Type u_4) [inst : EuclideanDomain R] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Field L] [algRL : Algebra R L] [inst_4 : Algebra R S] [inst_5 : Algebra S L] [ist : IsScalarTower R S L] [iic : IsIntegralClosure S R L] {abv : AbsoluteValue R ℤ} {ι : Type u_5} [inst_6 : DecidableEq ι] [inst_7 : Fintype ι] (bS : Basis ι R S) (adm : abv.IsAdmissible) [inst_8 : Infinite R] [inst_9 : DecidableEq R] [inst_10 : Algebra.IsAlgebraic R L] (a : S) {b : S}, b ≠ 0 → ∃ q, ∃ r ∈ ClassGroup.finsetApprox bS adm, abv ((Algebra.norm R) (r • a - q * b)) < abv ((Algebra.norm R) b)
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About
Loogle searches of Lean and Mathlib definitions and theorems.
You may also want to try the CLI version, the 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 currently provided by Joachim Breitner <mail@joachim-breitner.de>.
This is Loogle revision fa2ddf5
serving mathlib revision 38aa2fc