Loogle!

Result

Found 6 declarations mentioning ConvexCone.map.

• ConvexCone.map_id 📋 Mathlib.Geometry.Convex.Cone.Basic
  {R : Type u_2} {M : Type u_4} [Semiring R] [PartialOrder R] [AddCommMonoid M] [Module R M] (C : ConvexCone R M) : ConvexCone.map LinearMap.id C = C
• ConvexCone.map 📋 Mathlib.Geometry.Convex.Cone.Basic
  {R : Type u_2} {M : Type u_4} {N : Type u_5} [Semiring R] [PartialOrder R] [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N] (f : M →ₗ[R] N) (C : ConvexCone R M) : ConvexCone R N
• ConvexCone.map_map 📋 Mathlib.Geometry.Convex.Cone.Basic
  {R : Type u_2} {M : Type u_4} {N : Type u_5} {O : Type u_6} [Semiring R] [PartialOrder R] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid O] [Module R M] [Module R N] [Module R O] (g : N →ₗ[R] O) (f : M →ₗ[R] N) (C : ConvexCone R M) : ConvexCone.map g (ConvexCone.map f C) = ConvexCone.map (g ∘ₗ f) C
• ConvexCone.coe_map 📋 Mathlib.Geometry.Convex.Cone.Basic
  {R : Type u_2} {M : Type u_4} {N : Type u_5} [Semiring R] [PartialOrder R] [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N] (C : ConvexCone R M) (f : M →ₗ[R] N) : ↑(ConvexCone.map f C) = ⇑f '' ↑C
• ConvexCone.mem_map 📋 Mathlib.Geometry.Convex.Cone.Basic
  {R : Type u_2} {M : Type u_4} {N : Type u_5} [Semiring R] [PartialOrder R] [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N] {f : M →ₗ[R] N} {C : ConvexCone R M} {y : N} : y ∈ ConvexCone.map f C ↔ ∃ x ∈ C, f x = y
• PointedCone.toConvexCone_map 📋 Mathlib.Geometry.Convex.Cone.Pointed
  {R : Type u_1} {E : Type u_2} {F : Type u_3} [Semiring R] [PartialOrder R] [IsOrderedRing R] [AddCommMonoid E] [Module R E] [AddCommMonoid F] [Module R F] (C : PointedCone R E) (f : E →ₗ[R] F) : ↑(PointedCone.map f C) = ConvexCone.map f ↑C

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 2c2d6a2 serving mathlib revision 288ffbb