Loogle!
Result
Found 19 declarations mentioning Lattice.toSemilatticeSup, CompleteLattice.toLattice, PartialOrder.toPreorder, Preorder.toLE, TopologicalSpace.instCompleteLattice, CompleteLattice.toBoundedOrder, TopologicalSpace, OrderTop.toTop, BoundedOrder.toOrderTop, SemilatticeSup.toPartialOrder, and Top.top. Of these, 19 match your pattern(s).
- inseparable_top π Mathlib.Topology.Order
{Ξ± : Type u} (x y : Ξ±) : Inseparable x y - continuous_top π Mathlib.Topology.Order
{Ξ± : Type u} {Ξ² : Type v} {f : Ξ± β Ξ²} {t : TopologicalSpace Ξ±} : Continuous f - nhds_top π Mathlib.Topology.Order
{Ξ± : Type u} {a : Ξ±} : nhds a = β€ - induced_const π Mathlib.Topology.Order
{Ξ± : Type u_1} {Ξ² : Type u_2} [t : TopologicalSpace Ξ±] {x : Ξ±} : TopologicalSpace.induced (fun x_1 => x) t = β€ - TopologicalSpace.eq_top_iff_forall_inseparable π Mathlib.Topology.Order
{Ξ± : Type u} {t : TopologicalSpace Ξ±} : t = β€ β β (x y : Ξ±), Inseparable x y - TopologicalSpace.ne_top_iff_exists_not_inseparable π Mathlib.Topology.Order
{Ξ± : Type u} {t : TopologicalSpace Ξ±} : t β β€ β β x y, Β¬Inseparable x y - TopologicalSpace.isOpen_top_iff π Mathlib.Topology.Order
{Ξ± : Type u_2} (U : Set Ξ±) : IsOpen U β U = β β¨ U = Set.univ - induced_top π Mathlib.Topology.Order
{Ξ± : Type u_1} {Ξ² : Type u_2} {g : Ξ² β Ξ±} : TopologicalSpace.induced g β€ = β€ - SeparationQuotient.nontrivial_iff π Mathlib.Topology.Inseparable
{Ξ± : Type u_4} {t : TopologicalSpace Ξ±} : Nontrivial (SeparationQuotient Ξ±) β t β β€ - SeparationQuotient.subsingleton_iff π Mathlib.Topology.Inseparable
{Ξ± : Type u_4} {t : TopologicalSpace Ξ±} : Subsingleton (SeparationQuotient Ξ±) β t = β€ - SeparationQuotient.inseparableSetoid_eq_top_iff π Mathlib.Topology.Inseparable
{Ξ± : Type u_4} {t : TopologicalSpace Ξ±} : inseparableSetoid Ξ± = β€ β t = β€ - AddGroupTopology.toTopologicalSpace_top π Mathlib.Topology.Algebra.Group.GroupTopology
{Ξ± : Type u} [AddGroup Ξ±] : β€.toTopologicalSpace = β€ - GroupTopology.toTopologicalSpace_top π Mathlib.Topology.Algebra.Group.GroupTopology
{Ξ± : Type u} [Group Ξ±] : β€.toTopologicalSpace = β€ - AddGroupTopology.instTop.eq_1 π Mathlib.Topology.Algebra.Group.GroupTopology
{Ξ± : Type u} [AddGroup Ξ±] : AddGroupTopology.instTop = { top := { toTopologicalSpace := β€, toIsTopologicalAddGroup := β― } } - GroupTopology.instTop.eq_1 π Mathlib.Topology.Algebra.Group.GroupTopology
{Ξ± : Type u} [Group Ξ±] : GroupTopology.instTop = { top := { toTopologicalSpace := β€, toIsTopologicalGroup := β― } } - UniformSpace.toTopologicalSpace_top π Mathlib.Topology.UniformSpace.Basic
{Ξ± : Type ua} : β€.toTopologicalSpace = β€ - TopologicalSpace.Opens.eq_bot_or_top π Mathlib.Topology.Sets.Opens
{Ξ± : Type u_5} [t : TopologicalSpace Ξ±] (h : t = β€) (U : TopologicalSpace.Opens Ξ±) : U = β₯ β¨ U = β€ - TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscrete π Mathlib.Topology.Sheaves.PUnit
{C : Type u} [CategoryTheory.Category.{v, u} C] {X : TopCat} (hind : X.str = β€) (F : TopCat.Presheaf C X) (it : CategoryTheory.Limits.IsTerminal (F.obj (Opposite.op β₯))) : F.IsSheaf - TopCat.Presheaf.isSheaf_iff_isTerminal_of_indiscrete π Mathlib.Topology.Sheaves.PUnit
{C : Type u} [CategoryTheory.Category.{v, u} C] {X : TopCat} (hind : X.str = β€) (F : TopCat.Presheaf C X) : F.IsSheaf β Nonempty (CategoryTheory.Limits.IsTerminal (F.obj (Opposite.op β₯)))
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:
By constant:
πReal.sin
finds all lemmas whose statement somehow mentions the sine function.By lemma name substring:
π"differ"
finds all lemmas that have"differ"
somewhere in their lemma name.By subexpression:
π_ * (_ ^ _)
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
πReal.sqrt ?a * Real.sqrt ?a
If the pattern has parameters, they are matched in any order. Both of these will find
List.map
:
π(?a -> ?b) -> List ?a -> List ?b
πList ?a -> (?a -> ?b) -> List ?b
By main conclusion:
π|- tsum _ = _ * tsum _
finds all lemmas where the conclusion (the subexpression to the right of allβ
andβ
) 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,
π|- _ < _ β 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
π Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ β _
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 06e7f72
serving mathlib revision 8e2d951