Loogle!

Result

Found 9 declarations mentioning Submodule.baseChange.

• Submodule.baseChange 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} (A : Type u_3) [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] (p : Submodule R M) : Submodule A (TensorProduct R A M)
• Submodule.baseChange_bot 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} (A : Type u_3) [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] : Submodule.baseChange A ⊥ = ⊥
• Submodule.baseChange_top 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} (A : Type u_3) [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] : Submodule.baseChange A ⊤ = ⊤
• Submodule.tmul_mem_baseChange_of_mem 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} {A : Type u_3} [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] {p : Submodule R M} (a : A) {m : M} (hm : m ∈ p) : a ⊗ₜ[R] m ∈ Submodule.baseChange A p
• Submodule.baseChange.eq_1 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} (A : Type u_3) [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] (p : Submodule R M) : Submodule.baseChange A p = (LinearMap.baseChange A p.subtype).range
• Submodule.baseChange_span 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} (A : Type u_3) [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] (s : Set M) : Submodule.baseChange A (Submodule.span R s) = Submodule.span A (⇑((TensorProduct.mk R A M) 1) '' s)
• Submodule.baseChange_eq_span 📋 Mathlib.LinearAlgebra.TensorProduct.Tower
  {R : Type u_1} {M : Type u_2} (A : Type u_3) [CommSemiring R] [Semiring A] [Algebra R A] [AddCommMonoid M] [Module R M] (p : Submodule R M) : Submodule.baseChange A p = Submodule.span A ↑(Submodule.map ((TensorProduct.mk R A M) 1) p)
• LieSubmodule.coe_baseChange 📋 Mathlib.Algebra.Lie.BaseChange
  (R : Type u_1) (A : Type u_2) (L : Type u_3) (M : Type u_4) [CommRing R] [LieRing L] [LieAlgebra R L] [AddCommGroup M] [Module R M] [LieRingModule L M] [LieModule R L M] [CommRing A] [Algebra R A] (N : LieSubmodule R L M) : ↑(LieSubmodule.baseChange A N) = Submodule.baseChange A ↑N
• LieSubmodule.baseChange.eq_1 📋 Mathlib.Algebra.Lie.BaseChange
  {R : Type u_1} (A : Type u_2) {L : Type u_3} {M : Type u_4} [CommRing R] [LieRing L] [LieAlgebra R L] [AddCommGroup M] [Module R M] [LieRingModule L M] [LieModule R L M] [CommRing A] [Algebra R A] (N : LieSubmodule R L M) : LieSubmodule.baseChange A N = { toSubmodule := Submodule.baseChange A ↑N, lie_mem := ⋯ }

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 6ff4759 serving mathlib revision 519f454