Theorems · Theorem · group theory

AddMonoidHom.mclosure_range

∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {F : Type u_4}
  [inst_2 : FunLike F M N] [mc : AddMonoidHomClass F M N] (f : F),
  AddSubmonoid.closure (Set.range ⇑f) = AddMonoidHom.mrange f

Defined in: Mathlib.Algebra.Group.Submonoid.Operations
Cited by: 0 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddZeroClass AddZeroClass FunLike AddMonoidHomClass

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Setproof · cited by 53,352
Top.topproof · cited by 9,680
Set.rangestatement · cited by 4,705
Set.univproof · cited by 3,945
FunLikestatement and proof · cited by 2,560
AddZeroClassstatement and proof · cited by 1,237
AddSubmonoidstatement and proof · cited by 1,178
Set.image_univproof · cited by 322
AddMonoidHomClassstatement and proof · cited by 252
AddSubmonoid.closurestatement and proof · cited by 224
AddSubmonoid.mapproof · cited by 99

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