Loogle!

Result

Found 15 declarations mentioning Submonoid.LocalizationMap.map.

• Submonoid.LocalizationMap.map 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] (k : T.LocalizationMap Q) : N →* Q
• Submonoid.LocalizationMap.map.eq_1 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] (k : T.LocalizationMap Q) : f.map hy k = f.lift ⋯
• Submonoid.LocalizationMap.map_comp 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} : (f.map hy k).comp f.toMap = k.toMap.comp g
• Submonoid.LocalizationMap.map_injective_of_injective 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {Q : Type u_4} [CommMonoid Q] (hg : Function.Injective ⇑g) (k : (Submonoid.map g S).LocalizationMap Q) : Function.Injective ⇑(f.map ⋯ k)
• Submonoid.LocalizationMap.map_surjective_of_surjective 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {Q : Type u_4} [CommMonoid Q] (hg : Function.Surjective ⇑g) (k : (Submonoid.map g S).LocalizationMap Q) : Function.Surjective ⇑(f.map ⋯ k)
• Submonoid.LocalizationMap.map_eq 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} (x : M) : (f.map hy k) (f.toMap x) = k.toMap (g x)
• Submonoid.LocalizationMap.map_mk' 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} (x : M) (y : ↥S) : (f.map hy k) (f.mk' x y) = k.mk' (g x) ⟨g ↑y, ⋯⟩
• Submonoid.LocalizationMap.map_mul_left 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} (z : N) : k.toMap (g ↑(f.sec z).2) * (f.map hy k) z = k.toMap (g (f.sec z).1)
• Submonoid.LocalizationMap.map_mul_right 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} (z : N) : (f.map hy k) z * k.toMap (g ↑(f.sec z).2) = k.toMap (g (f.sec z).1)
• Submonoid.LocalizationMap.map_spec 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} (z : N) (u : Q) : (f.map hy k) z = u ↔ k.toMap (g (f.sec z).1) = k.toMap (g ↑(f.sec z).2) * u
• Submonoid.LocalizationMap.map_id 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] (f : S.LocalizationMap N) (z : N) : (f.map ⋯ f) z = z
• Submonoid.LocalizationMap.map_comp_map 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} {A : Type u_5} [CommMonoid A] {U : Submonoid A} {R : Type u_6} [CommMonoid R] (j : U.LocalizationMap R) {l : P →* A} (hl : ∀ (w : ↥T), l ↑w ∈ U) : (k.map hl j).comp (f.map hy k) = f.map ⋯ j
• Submonoid.LocalizationMap.map_map 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {g : M →* P} {T : Submonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T) {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} {A : Type u_5} [CommMonoid A] {U : Submonoid A} {R : Type u_6} [CommMonoid R] (j : U.LocalizationMap R) {l : P →* A} (hl : ∀ (w : ↥T), l ↑w ∈ U) (x : N) : (k.map hl j) ((f.map hy k) x) = (f.map ⋯ j) x
• Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {T : Submonoid P} {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} {j : M ≃* P} (H : Submonoid.map j.toMonoidHom S = T) : (f.mulEquivOfMulEquiv k H).toMonoidHom = f.map ⋯ k
• Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map_apply 📋 Mathlib.GroupTheory.MonoidLocalization.Basic
  {M : Type u_1} [CommMonoid M] {S : Submonoid M} {N : Type u_2} [CommMonoid N] {P : Type u_3} [CommMonoid P] (f : S.LocalizationMap N) {T : Submonoid P} {Q : Type u_4} [CommMonoid Q] {k : T.LocalizationMap Q} {j : M ≃* P} (H : Submonoid.map j.toMonoidHom S = T) (x : N) : (f.mulEquivOfMulEquiv k H) x = (f.map ⋯ k) x

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 19971e9 serving mathlib revision bce1d65