Loogle!
Result
Found 9630 declarations mentioning Equiv. Of these, 45 have a name containing "curry".
- Equiv.curry ๐ Mathlib.Logic.Equiv.Prod
(ฮฑ : Type u_9) (ฮฒ : Type u_10) (ฮณ : Sort u_11) : (ฮฑ ร ฮฒ โ ฮณ) โ (ฮฑ โ ฮฒ โ ฮณ) - Equiv.curry_apply ๐ Mathlib.Logic.Equiv.Prod
(ฮฑ : Type u_9) (ฮฒ : Type u_10) (ฮณ : Sort u_11) : โ(Equiv.curry ฮฑ ฮฒ ฮณ) = Function.curry - Equiv.curry_symm_apply ๐ Mathlib.Logic.Equiv.Prod
(ฮฑ : Type u_9) (ฮฒ : Type u_10) (ฮณ : Sort u_11) : โ(Equiv.curry ฮฑ ฮฒ ฮณ).symm = Function.uncurry - Equiv.piCurry ๐ Mathlib.Logic.Equiv.Basic
{ฮฑ : Type u_11} {ฮฒ : ฮฑ โ Type u_9} (ฮณ : (a : ฮฑ) โ ฮฒ a โ Type u_10) : ((x : (i : ฮฑ) ร ฮฒ i) โ ฮณ x.fst x.snd) โ ((a : ฮฑ) โ (b : ฮฒ a) โ ฮณ a b) - Equiv.piCurry_apply ๐ Mathlib.Logic.Equiv.Basic
{ฮฑ : Type u_11} {ฮฒ : ฮฑ โ Type u_9} (ฮณ : (a : ฮฑ) โ ฮฒ a โ Type u_10) (f : (x : (i : ฮฑ) ร ฮฒ i) โ ฮณ x.fst x.snd) : (Equiv.piCurry ฮณ) f = Sigma.curry f - Equiv.piCurry_symm_apply ๐ Mathlib.Logic.Equiv.Basic
{ฮฑ : Type u_11} {ฮฒ : ฮฑ โ Type u_9} (ฮณ : (a : ฮฑ) โ ฮฒ a โ Type u_10) (f : (a : ฮฑ) โ (b : ฮฒ a) โ ฮณ a b) : (Equiv.piCurry ฮณ).symm f = Sigma.uncurry f - DFinsupp.sigmaCurryEquiv ๐ Mathlib.Data.DFinsupp.Sigma
{ฮน : Type u} {ฮฑ : ฮน โ Type u_2} {ฮด : (i : ฮน) โ ฮฑ i โ Type v} [(i : ฮน) โ (j : ฮฑ i) โ Zero (ฮด i j)] [DecidableEq ฮน] : (ฮ โ (i : (x : ฮน) ร ฮฑ x), ฮด i.fst i.snd) โ ฮ โ (i : ฮน) (j : ฮฑ i), ฮด i j - DFinsupp.sigmaCurryLEquiv_apply ๐ Mathlib.LinearAlgebra.DFinsupp
{ฮน : Type u_1} {R : Type u_3} [Semiring R] {ฮฑ : ฮน โ Type u_7} {M : (i : ฮน) โ ฮฑ i โ Type u_8} [(i : ฮน) โ (j : ฮฑ i) โ AddCommMonoid (M i j)] [(i : ฮน) โ (j : ฮฑ i) โ Module R (M i j)] [DecidableEq ฮน] (aโ : ฮ โ (i : (x : ฮน) ร ฮฑ x), M i.fst i.snd) : DFinsupp.sigmaCurryLEquiv aโ = DFinsupp.sigmaCurryEquiv aโ - DFinsupp.sigmaCurryLEquiv_symm_apply ๐ Mathlib.LinearAlgebra.DFinsupp
{ฮน : Type u_1} {R : Type u_3} [Semiring R] {ฮฑ : ฮน โ Type u_7} {M : (i : ฮน) โ ฮฑ i โ Type u_8} [(i : ฮน) โ (j : ฮฑ i) โ AddCommMonoid (M i j)] [(i : ฮน) โ (j : ฮฑ i) โ Module R (M i j)] [DecidableEq ฮน] (aโ : ฮ โ (i : ฮน) (j : ฮฑ i), M i j) : DFinsupp.sigmaCurryLEquiv.symm aโ = DFinsupp.sigmaCurryEquiv.symm aโ - CategoryTheory.Functor.curryingEquiv ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] : CategoryTheory.Functor C (CategoryTheory.Functor D E) โ CategoryTheory.Functor (C ร D) E - CategoryTheory.Functor.curryingFlipEquiv ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] : CategoryTheory.Functor D (CategoryTheory.Functor C E) โ CategoryTheory.Functor (C ร D) E - CategoryTheory.Functor.curryingEquiv_apply_obj ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (F : CategoryTheory.Functor C (CategoryTheory.Functor D E)) (X : C ร D) : (CategoryTheory.Functor.curryingEquiv F).obj X = (F.obj X.1).obj X.2 - CategoryTheory.Functor.curryingFlipEquiv_apply_obj ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (aโ : CategoryTheory.Functor D (CategoryTheory.Functor C E)) (X : C ร D) : (CategoryTheory.Functor.curryingFlipEquiv aโ).obj X = (aโ.obj X.2).obj X.1 - CategoryTheory.Functor.curryingEquiv_symm_apply_obj_obj ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (G : CategoryTheory.Functor (C ร D) E) (X : C) (Y : D) : ((CategoryTheory.Functor.curryingEquiv.symm G).obj X).obj Y = G.obj (X, Y) - CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_obj ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (aโ : CategoryTheory.Functor (C ร D) E) (k : D) (j : C) : ((CategoryTheory.Functor.curryingFlipEquiv.symm aโ).obj k).obj j = aโ.obj (j, k) - CategoryTheory.Functor.curryingEquiv_symm_apply_obj_map ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (G : CategoryTheory.Functor (C ร D) E) (X : C) {Xโ Yโ : D} (g : Xโ โถ Yโ) : ((CategoryTheory.Functor.curryingEquiv.symm G).obj X).map g = G.map (CategoryTheory.CategoryStruct.id X, g) - CategoryTheory.Functor.curryingEquiv_apply_map ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (F : CategoryTheory.Functor C (CategoryTheory.Functor D E)) {X Y : C ร D} (f : X โถ Y) : (CategoryTheory.Functor.curryingEquiv F).map f = CategoryTheory.CategoryStruct.comp ((F.map f.1).app X.2) ((F.obj Y.1).map f.2) - CategoryTheory.Functor.curryingEquiv_symm_apply_map_app ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (G : CategoryTheory.Functor (C ร D) E) {Xโ Yโ : C} (f : Xโ โถ Yโ) (Y : D) : ((CategoryTheory.Functor.curryingEquiv.symm G).map f).app Y = G.map (f, CategoryTheory.CategoryStruct.id Y) - CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_map ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (aโ : CategoryTheory.Functor (C ร D) E) (k : D) {Xโ Yโ : C} (f : Xโ โถ Yโ) : ((CategoryTheory.Functor.curryingFlipEquiv.symm aโ).obj k).map f = aโ.map (f, CategoryTheory.CategoryStruct.id k) - CategoryTheory.Functor.curryingFlipEquiv_apply_map ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (aโ : CategoryTheory.Functor D (CategoryTheory.Functor C E)) {X Y : C ร D} (f : X โถ Y) : (CategoryTheory.Functor.curryingFlipEquiv aโ).map f = CategoryTheory.CategoryStruct.comp ((aโ.map f.2).app X.1) ((aโ.obj Y.2).map f.1) - CategoryTheory.Functor.curryingFlipEquiv_symm_apply_map_app ๐ Mathlib.CategoryTheory.Functor.Currying
{C : Type uโ} [CategoryTheory.Category.{vโ, uโ} C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] {E : Type uโ} [CategoryTheory.Category.{vโ, uโ} E] (aโ : CategoryTheory.Functor (C ร D) E) {Xโ Yโ : D} (f : Xโ โถ Yโ) (j : C) : ((CategoryTheory.Functor.curryingFlipEquiv.symm aโ).map f).app j = aโ.map (CategoryTheory.CategoryStruct.id j, f) - CategoryTheory.MonoidalClosed.curryHomEquiv' ๐ Mathlib.CategoryTheory.Closed.Monoidal
{C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.MonoidalCategory C] {X Y : C} [CategoryTheory.Closed X] : (X โถ Y) โ (CategoryTheory.MonoidalCategoryStruct.tensorUnit C โถ (CategoryTheory.ihom X).obj Y) - CategoryTheory.MonoidalClosed.curryHomEquiv'_apply ๐ Mathlib.CategoryTheory.Closed.Monoidal
{C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.MonoidalCategory C] {X Y : C} [CategoryTheory.Closed X] (f : X โถ Y) : CategoryTheory.MonoidalClosed.curryHomEquiv' f = CategoryTheory.MonoidalClosed.curry' f - CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply ๐ Mathlib.CategoryTheory.Closed.Monoidal
{C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.MonoidalCategory C] {X Y : C} [CategoryTheory.Closed X] (g : CategoryTheory.MonoidalCategoryStruct.tensorUnit C โถ (CategoryTheory.ihom X).obj Y) : CategoryTheory.MonoidalClosed.curryHomEquiv'.symm g = CategoryTheory.MonoidalClosed.uncurry' g - CategoryTheory.MonoidalClosed.ofEquiv_curry_def ๐ Mathlib.CategoryTheory.Closed.Monoidal
{C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.MonoidalCategory C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] [CategoryTheory.MonoidalCategory D] (F : CategoryTheory.Functor C D) {G : CategoryTheory.Functor D C} (adj : F โฃ G) [F.Monoidal] [F.IsEquivalence] [CategoryTheory.MonoidalClosed D] {X Y Z : C} (f : CategoryTheory.MonoidalCategoryStruct.tensorObj X Y โถ Z) : CategoryTheory.MonoidalClosed.curry f = (adj.homEquiv Y ((CategoryTheory.ihom (F.obj X)).obj (F.obj Z))) (CategoryTheory.MonoidalClosed.curry ((adj.toEquivalence.symm.toAdjunction.homEquiv (CategoryTheory.MonoidalCategoryStruct.tensorObj (F.obj X) (F.obj Y)) Z) (CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.Monoidal.commTensorLeft F X).compInverseIso.hom.app Y) f))) - CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def ๐ Mathlib.CategoryTheory.Closed.Monoidal
{C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.MonoidalCategory C] {D : Type uโ} [CategoryTheory.Category.{vโ, uโ} D] [CategoryTheory.MonoidalCategory D] (F : CategoryTheory.Functor C D) {G : CategoryTheory.Functor D C} (adj : F โฃ G) [F.Monoidal] [F.IsEquivalence] [CategoryTheory.MonoidalClosed D] {X Y Z : C} (f : Y โถ (CategoryTheory.ihom X).obj Z) : CategoryTheory.MonoidalClosed.uncurry f = CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.Monoidal.commTensorLeft F X).compInverseIso.inv.app Y) ((adj.toEquivalence.symm.toAdjunction.homEquiv ((F.comp (CategoryTheory.MonoidalCategory.tensorLeft (F.obj X))).obj Y) Z).symm (CategoryTheory.MonoidalClosed.uncurry ((adj.homEquiv Y ((CategoryTheory.ihom (F.obj X)).obj (adj.toEquivalence.symm.inverse.obj Z))).symm f))) - MultilinearMap.curryFinFinset_apply ๐ Mathlib.LinearAlgebra.Multilinear.Curry
{R : Type uR} {Mโ : Type vโ} {M' : Type v'} [CommSemiring R] [AddCommMonoid M'] [AddCommMonoid Mโ] [Module R M'] [Module R Mโ] {k l n : โ} {s : Finset (Fin n)} (hk : s.card = k) (hl : sแถ.card = l) (f : MultilinearMap R (fun x => M') Mโ) (mk : Fin k โ M') (ml : Fin l โ M') : (((MultilinearMap.curryFinFinset R Mโ M' hk hl) f) mk) ml = f fun i => Sum.elim mk ml ((finSumEquivOfFinset hk hl).symm i) - MultilinearMap.curryFinFinset_symm_apply ๐ Mathlib.LinearAlgebra.Multilinear.Curry
{R : Type uR} {Mโ : Type vโ} {M' : Type v'} [CommSemiring R] [AddCommMonoid M'] [AddCommMonoid Mโ] [Module R M'] [Module R Mโ] {k l n : โ} {s : Finset (Fin n)} (hk : s.card = k) (hl : sแถ.card = l) (f : MultilinearMap R (fun x => M') (MultilinearMap R (fun x => M') Mโ)) (m : Fin n โ M') : ((MultilinearMap.curryFinFinset R Mโ M' hk hl).symm f) m = (f fun i => m ((finSumEquivOfFinset hk hl) (Sum.inl i))) fun i => m ((finSumEquivOfFinset hk hl) (Sum.inr i)) - measurable_equivCurry ๐ Mathlib.MeasureTheory.MeasurableSpace.Constructions
{ฮน : Type u_6} {ฮบ : Type u_7} {X : Type u_8} [MeasurableSpace X] : Measurable โ(Equiv.curry ฮน ฮบ X) - measurable_equivCurry_symm ๐ Mathlib.MeasureTheory.MeasurableSpace.Constructions
{ฮน : Type u_6} {ฮบ : Type u_7} {X : Type u_8} [MeasurableSpace X] : Measurable โ(Equiv.curry ฮน ฮบ X).symm - measurable_piCurry ๐ Mathlib.MeasureTheory.MeasurableSpace.Constructions
{ฮน : Type u_6} {ฮบ : ฮน โ Type u_7} {X : (i : ฮน) โ ฮบ i โ Type u_8} [(i : ฮน) โ (j : ฮบ i) โ MeasurableSpace (X i j)] : Measurable โ(Equiv.piCurry X) - measurable_piCurry_symm ๐ Mathlib.MeasureTheory.MeasurableSpace.Constructions
{ฮน : Type u_6} {ฮบ : ฮน โ Type u_7} {X : (i : ฮน) โ ฮบ i โ Type u_8} [(i : ฮน) โ (j : ฮบ i) โ MeasurableSpace (X i j)] : Measurable โ(Equiv.piCurry X).symm - ContinuousMultilinearMap.curryFinFinset_apply ๐ Mathlib.Analysis.Normed.Module.Multilinear.Curry
{๐ : Type u} {n : โ} {G : Type wG} {G' : Type wG'} [NontriviallyNormedField ๐] [NormedAddCommGroup G] [NormedSpace ๐ G] [NormedAddCommGroup G'] [NormedSpace ๐ G'] {k l : โ} {s : Finset (Fin n)} (hk : s.card = k) (hl : sแถ.card = l) (f : ContinuousMultilinearMap ๐ (fun i => G) G') (mk : Fin k โ G) (ml : Fin l โ G) : (((ContinuousMultilinearMap.curryFinFinset ๐ G G' hk hl) f) mk) ml = f fun i => Sum.elim mk ml ((finSumEquivOfFinset hk hl).symm i) - ContinuousMultilinearMap.curryFinFinset_symm_apply ๐ Mathlib.Analysis.Normed.Module.Multilinear.Curry
{๐ : Type u} {n : โ} {G : Type wG} {G' : Type wG'} [NontriviallyNormedField ๐] [NormedAddCommGroup G] [NormedSpace ๐ G] [NormedAddCommGroup G'] [NormedSpace ๐ G'] {k l : โ} {s : Finset (Fin n)} (hk : s.card = k) (hl : sแถ.card = l) (f : ContinuousMultilinearMap ๐ (fun i => G) (ContinuousMultilinearMap ๐ (fun i => G) G')) (m : Fin n โ G) : ((ContinuousMultilinearMap.curryFinFinset ๐ G G' hk hl).symm f) m = (f fun i => m ((finSumEquivOfFinset hk hl) (Sum.inl i))) fun i => m ((finSumEquivOfFinset hk hl) (Sum.inr i)) - ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp ๐ Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin
{๐ : Type u_1} {E : Type u_2} {F : Type u_3} [NontriviallyNormedField ๐] [NormedAddCommGroup E] [NormedSpace ๐ E] [NormedAddCommGroup F] [NormedSpace ๐ F] (f : E โL[๐] F) : ContinuousAlternatingMap.alternatizeUncurryFin ((โ{ toLinearEquiv := (ContinuousAlternatingMap.constOfIsEmptyLIE ๐ E F (Fin 0)).toLinearEquiv, continuous_toFun := โฏ, continuous_invFun := โฏ }).comp f) = (ContinuousAlternatingMap.ofSubsingleton ๐ E F 0) f - Function.OfArity.curryEquiv ๐ Mathlib.Data.Fin.Tuple.Curry
{ฮฑ ฮฒ : Type u} (n : โ) : ((Fin n โ ฮฑ) โ ฮฒ) โ Function.OfArity ฮฑ ฮฒ n - Function.FromTypes.curryEquiv ๐ Mathlib.Data.Fin.Tuple.Curry
{n : โ} {ฯ : Type u} (p : Fin n โ Type u) : (((i : Fin n) โ p i) โ ฯ) โ Function.FromTypes p ฯ - Function.OfArity.curryEquiv_apply ๐ Mathlib.Data.Fin.Tuple.Curry
{ฮฑ ฮฒ : Type u} (n : โ) (aโ : (Fin n โ ฮฑ) โ ฮฒ) : (Function.OfArity.curryEquiv n) aโ = Function.FromTypes.curry aโ - Function.FromTypes.curryEquiv_apply ๐ Mathlib.Data.Fin.Tuple.Curry
{n : โ} {ฯ : Type u} (p : Fin n โ Type u) (aโ : ((i : Fin n) โ p i) โ ฯ) : (Function.FromTypes.curryEquiv p) aโ = Function.FromTypes.curry aโ - Function.OfArity.curryEquiv_symm_apply ๐ Mathlib.Data.Fin.Tuple.Curry
{ฮฑ ฮฒ : Type u} (n : โ) (f : Function.FromTypes (fun a => ฮฑ) ฮฒ) (aโ : Fin n โ ฮฑ) : (Function.OfArity.curryEquiv n).symm f aโ = f.uncurry aโ - Function.FromTypes.curryEquiv_symm_apply ๐ Mathlib.Data.Fin.Tuple.Curry
{n : โ} {ฯ : Type u} (p : Fin n โ Type u) (f : Function.FromTypes p ฯ) (aโ : (i : Fin n) โ p i) : (Function.FromTypes.curryEquiv p).symm f aโ = f.uncurry aโ - Function.OfArity.curry_two_eq_curry ๐ Mathlib.Data.Fin.Tuple.Curry
{ฮฑ ฮฒ : Type u} (f : (Fin 2 โ ฮฑ) โ ฮฒ) : Function.OfArity.curry f = Function.curry (f โ โ(finTwoArrowEquiv ฮฑ).symm) - Function.OfArity.uncurry_two_eq_uncurry ๐ Mathlib.Data.Fin.Tuple.Curry
{ฮฑ ฮฒ : Type u} (f : Function.OfArity ฮฑ ฮฒ 2) : f.uncurry = Function.uncurry f โ โ(finTwoArrowEquiv ฮฑ) - Function.FromTypes.uncurry_two_eq_uncurry ๐ Mathlib.Data.Fin.Tuple.Curry
(p : Fin 2 โ Type u) (ฯ : Type u) (f : Function.FromTypes p ฯ) : f.uncurry = Function.uncurry f โ โ(piFinTwoEquiv p) - Function.FromTypes.curry_two_eq_curry ๐ Mathlib.Data.Fin.Tuple.Curry
{p : Fin 2 โ Type u} {ฯ : Type u} (f : ((i : Fin 2) โ p i) โ ฯ) : Function.FromTypes.curry f = Function.curry (f โ โ(piFinTwoEquiv p).symm)
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:
๐Real.sin
finds all lemmas whose statement somehow mentions the sine function.By lemma name substring:
๐"differ"
finds all lemmas that have"differ"somewhere in their lemma name.By subexpression:
๐_ * (_ ^ _)
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
๐Real.sqrt ?a * Real.sqrt ?aIf the pattern has parameters, they are matched in any order. Both of these will find
List.map:
๐(?a -> ?b) -> List ?a -> List ?b
๐List ?a -> (?a -> ?b) -> List ?bBy main conclusion:
๐|- tsum _ = _ * tsum _
finds all lemmas where the conclusion (the subexpression to the right of allโandโ) 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,
๐|- _ < _ โ tsum _ < tsum _
will findtsum_lt_tsumeven though the hypothesisf i < g iis 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
๐ Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ โ _
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 0ac13cd serving mathlib revision 7a854fc