Loogle!

Result

Found 13 declarations mentioning TrivSqZeroExt.map.

TrivSqZeroExt.map 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) : TrivSqZeroExt R' M →ₐ[R'] TrivSqZeroExt R' N
TrivSqZeroExt.map_id 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] : TrivSqZeroExt.map LinearMap.id = AlgHom.id R' (TrivSqZeroExt R' M)
TrivSqZeroExt.fst_map 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) (x : TrivSqZeroExt R' M) : ((TrivSqZeroExt.map f) x).fst = x.fst
TrivSqZeroExt.map_inl 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) (r : R') : (TrivSqZeroExt.map f) (TrivSqZeroExt.inl r) = TrivSqZeroExt.inl r
TrivSqZeroExt.snd_map 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) (x : TrivSqZeroExt R' M) : ((TrivSqZeroExt.map f) x).snd = f x.snd
TrivSqZeroExt.map_inr 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) (x : M) : (TrivSqZeroExt.map f) (TrivSqZeroExt.inr x) = TrivSqZeroExt.inr (f x)
TrivSqZeroExt.map_comp_map 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} {P : Type u_4} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] [AddCommMonoid P] [Module R' P] [Module R'ᵐᵒᵖ P] [IsCentralScalar R' P] (f : M →ₗ[R'] N) (g : N →ₗ[R'] P) : TrivSqZeroExt.map (g ∘ₗ f) = (TrivSqZeroExt.map g).comp (TrivSqZeroExt.map f)
TrivSqZeroExt.map_comp_inlAlgHom 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) : (TrivSqZeroExt.map f).comp (TrivSqZeroExt.inlAlgHom R' R' M) = TrivSqZeroExt.inlAlgHom R' R' N
TrivSqZeroExt.sndHom_comp_map 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) : TrivSqZeroExt.sndHom R' N ∘ₗ (TrivSqZeroExt.map f).toLinearMap = f ∘ₗ TrivSqZeroExt.sndHom R' M
TrivSqZeroExt.map_comp_inrHom 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) : (TrivSqZeroExt.map f).toLinearMap ∘ₗ TrivSqZeroExt.inrHom R' M = TrivSqZeroExt.inrHom R' N ∘ₗ f
TrivSqZeroExt.fstHom_comp_map 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) : (TrivSqZeroExt.fstHom R' R' N).comp (TrivSqZeroExt.map f) = TrivSqZeroExt.fstHom R' R' M
TrivSqZeroExt.map.eq_1 📋 Mathlib.Algebra.TrivSqZeroExt
{R' : Type u} {M : Type v} [CommSemiring R'] [AddCommMonoid M] [Module R' M] [Module R'ᵐᵒᵖ M] [IsCentralScalar R' M] {N : Type u_3} [AddCommMonoid N] [Module R' N] [Module R'ᵐᵒᵖ N] [IsCentralScalar R' N] (f : M →ₗ[R'] N) : TrivSqZeroExt.map f = TrivSqZeroExt.liftEquivOfComm ⟨TrivSqZeroExt.inrHom R' N ∘ₗ f, ⋯⟩
ExteriorAlgebra.toTrivSqZeroExt_comp_map 📋 Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
{R : Type u1} [CommRing R] {M : Type u2} [AddCommGroup M] [Module R M] {N : Type u4} [AddCommGroup N] [Module R N] [Module Rᵐᵒᵖ M] [IsCentralScalar R M] [Module Rᵐᵒᵖ N] [IsCentralScalar R N] (f : M →ₗ[R] N) : ExteriorAlgebra.toTrivSqZeroExt.comp (ExteriorAlgebra.map f) = (TrivSqZeroExt.map f).comp ExteriorAlgebra.toTrivSqZeroExt

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 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 19971e9 serving mathlib revision bce1d65