Loogle!

Result

Found 11 declarations mentioning AddUnits.map.

• AddUnits.map 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} [AddMonoid M] [AddMonoid N] (f : M →+ N) : AddUnits M →+ AddUnits N
• AddUnits.map_id 📋 Mathlib.Algebra.Group.Units.Hom
  (M : Type u) [AddMonoid M] : AddUnits.map (AddMonoidHom.id M) = AddMonoidHom.id (AddUnits M)
• AddUnits.map_injective 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} [AddMonoid M] [AddMonoid N] {f : M →+ N} (hf : Function.Injective ⇑f) : Function.Injective ⇑(AddUnits.map f)
• AddUnits.map_comp 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} {P : Type w} [AddMonoid M] [AddMonoid N] [AddMonoid P] (f : M →+ N) (g : N →+ P) : AddUnits.map (g.comp f) = (AddUnits.map g).comp (AddUnits.map f)
• AddUnits.coe_map 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} [AddMonoid M] [AddMonoid N] (f : M →+ N) (x : AddUnits M) : ↑((AddUnits.map f) x) = f ↑x
• AddUnits.coe_map_neg 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} [AddMonoid M] [AddMonoid N] (f : M →+ N) (u : AddUnits M) : ↑(-(AddUnits.map f) u) = f ↑(-u)
• AddUnits.map.eq_1 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} [AddMonoid M] [AddMonoid N] (f : M →+ N) : AddUnits.map f = AddMonoidHom.mk' (fun u => { val := f ↑u, neg := f u.neg, val_neg := ⋯, neg_val := ⋯ }) ⋯
• AddUnits.map_mk 📋 Mathlib.Algebra.Group.Units.Hom
  {M : Type u} {N : Type v} [AddMonoid M] [AddMonoid N] (f : M →+ N) (val inv : M) (val_inv : val + inv = 0) (inv_val : inv + val = 0) : (AddUnits.map f) { val := val, neg := inv, val_neg := val_inv, neg_val := inv_val } = { val := f val, neg := f inv, val_neg := ⋯, neg_val := ⋯ }
• AddEquiv.prodAddUnits.eq_1 📋 Mathlib.Algebra.Group.Prod
  {M : Type u_3} {N : Type u_4} [AddMonoid M] [AddMonoid N] : AddEquiv.prodAddUnits = { toFun := ⇑((AddUnits.map (AddMonoidHom.fst M N)).prod (AddUnits.map (AddMonoidHom.snd M N))), invFun := fun u => { val := (↑u.1, ↑u.2), neg := (↑(-u.1), ↑(-u.2)), val_neg := ⋯, neg_val := ⋯ }, left_inv := ⋯, right_inv := ⋯, map_add' := ⋯ }
• addUnitsCenterToCenterAddUnits.eq_1 📋 Mathlib.GroupTheory.Submonoid.Center
  (M : Type u_1) [AddMonoid M] : addUnitsCenterToCenterAddUnits M = (AddUnits.map (AddSubmonoid.center M).subtype).codRestrict (AddSubmonoid.center (AddUnits M)) ⋯
• Continuous.addUnits_map 📋 Mathlib.Topology.Algebra.Monoid
  {M : Type u_3} {N : Type u_4} [AddMonoid M] [AddMonoid N] [TopologicalSpace M] [TopologicalSpace N] (f : M →+ N) (hf : Continuous ⇑f) : Continuous ⇑(AddUnits.map f)

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