Loogle!

Result

Found 6 declarations mentioning Module.Ray.map.

• Module.Ray.map_refl 📋 Mathlib.LinearAlgebra.Ray
  {R : Type u_1} [CommSemiring R] [PartialOrder R] [IsStrictOrderedRing R] {M : Type u_2} [AddCommMonoid M] [Module R M] : Module.Ray.map (LinearEquiv.refl R M) = Equiv.refl (Module.Ray R M)
• Module.Ray.map 📋 Mathlib.LinearAlgebra.Ray
  {R : Type u_1} [CommSemiring R] [PartialOrder R] [IsStrictOrderedRing R] {M : Type u_2} [AddCommMonoid M] [Module R M] {N : Type u_3} [AddCommMonoid N] [Module R N] (e : M ≃ₗ[R] N) : Module.Ray R M ≃ Module.Ray R N
• Module.Ray.map_symm 📋 Mathlib.LinearAlgebra.Ray
  {R : Type u_1} [CommSemiring R] [PartialOrder R] [IsStrictOrderedRing R] {M : Type u_2} [AddCommMonoid M] [Module R M] {N : Type u_3} [AddCommMonoid N] [Module R N] (e : M ≃ₗ[R] N) : (Module.Ray.map e).symm = Module.Ray.map e.symm
• Module.Ray.map_neg 📋 Mathlib.LinearAlgebra.Ray
  {R : Type u_1} [CommRing R] [PartialOrder R] [IsStrictOrderedRing R] {M : Type u_2} {N : Type u_3} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N] (f : M ≃ₗ[R] N) (v : Module.Ray R M) : (Module.Ray.map f) (-v) = -(Module.Ray.map f) v
• Module.Ray.map_apply 📋 Mathlib.LinearAlgebra.Ray
  {R : Type u_1} [CommSemiring R] [PartialOrder R] [IsStrictOrderedRing R] {M : Type u_2} [AddCommMonoid M] [Module R M] {N : Type u_3} [AddCommMonoid N] [Module R N] (e : M ≃ₗ[R] N) (v : M) (hv : v ≠ 0) : (Module.Ray.map e) (rayOfNeZero R v hv) = rayOfNeZero R (e v) ⋯
• Module.Ray.linearEquiv_smul_eq_map 📋 Mathlib.LinearAlgebra.Ray
  {R : Type u_1} [CommSemiring R] [PartialOrder R] [IsStrictOrderedRing R] {M : Type u_2} [AddCommMonoid M] [Module R M] (e : M ≃ₗ[R] M) (v : Module.Ray R M) : e • v = (Module.Ray.map e) 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:

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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 8e80836 serving mathlib revision 1a37cd3