Loogle!
Result
Found 5 declarations mentioning Projectivization.map.
- Projectivization.map_id 📋 Mathlib.LinearAlgebra.Projectivization.Basic
{K : Type u_1} {V : Type u_2} [DivisionRing K] [AddCommGroup V] [Module K V] : Projectivization.map LinearMap.id ⋯ = id - Projectivization.map 📋 Mathlib.LinearAlgebra.Projectivization.Basic
{K : Type u_1} {V : Type u_2} [DivisionRing K] [AddCommGroup V] [Module K V] {L : Type u_3} {W : Type u_4} [DivisionRing L] [AddCommGroup W] [Module L W] {σ : K →+* L} (f : V →ₛₗ[σ] W) (hf : Function.Injective ⇑f) : Projectivization K V → Projectivization L W - Projectivization.map_injective 📋 Mathlib.LinearAlgebra.Projectivization.Basic
{K : Type u_1} {V : Type u_2} [DivisionRing K] [AddCommGroup V] [Module K V] {L : Type u_3} {W : Type u_4} [DivisionRing L] [AddCommGroup W] [Module L W] {σ : K →+* L} {τ : L →+* K} [RingHomInvPair σ τ] (f : V →ₛₗ[σ] W) (hf : Function.Injective ⇑f) : Function.Injective (Projectivization.map f hf) - Projectivization.map_comp 📋 Mathlib.LinearAlgebra.Projectivization.Basic
{K : Type u_1} {V : Type u_2} [DivisionRing K] [AddCommGroup V] [Module K V] {L : Type u_3} {W : Type u_4} [DivisionRing L] [AddCommGroup W] [Module L W] {F : Type u_5} {U : Type u_6} [DivisionRing F] [AddCommGroup U] [Module F U] {σ : K →+* L} {τ : L →+* F} {γ : K →+* F} [RingHomCompTriple σ τ γ] (f : V →ₛₗ[σ] W) (hf : Function.Injective ⇑f) (g : W →ₛₗ[τ] U) (hg : Function.Injective ⇑g) (hgf : Function.Injective ⇑(g ∘ₛₗ f) := ⋯) : Projectivization.map (g ∘ₛₗ f) hgf = Projectivization.map g hg ∘ Projectivization.map f hf - Projectivization.map_mk 📋 Mathlib.LinearAlgebra.Projectivization.Basic
{K : Type u_1} {V : Type u_2} [DivisionRing K] [AddCommGroup V] [Module K V] {L : Type u_3} {W : Type u_4} [DivisionRing L] [AddCommGroup W] [Module L W] {σ : K →+* L} (f : V →ₛₗ[σ] W) (hf : Function.Injective ⇑f) (v : V) (hv : v ≠ 0) : Projectivization.map f hf (Projectivization.mk K v hv) = Projectivization.mk L (f v) ⋯
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:
🔍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, _ * _, _ ^ _, |- _ < _ → _
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 19971e9
serving mathlib revision bce1d65