Mathlib Map

Theorems · Theorem · group theory

AddSubmonoid.map_strictMono_of_injective

∀ {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},
  Function.Injective ⇑f → StrictMono (AddSubmonoid.map f)
Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
0 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
AddZeroClassAddZeroClassFunLikeAddMonoidHomClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidStrictMono · cited by 706StrictMonoAddMonoidHomClass · cited by 252AddMonoidHomClassAddSubmonoid.map · cited by 99AddSubmonoid.mapGaloisCoinsertion.strictMono_l · cited by 10GaloisCoinsertion.strictM…AddSubmonoid.gciMapComap · cited by 9AddSubmonoid.gciMapComapAddSubmonoid.map_strictMono_o…CITED BYCITES

Cites9

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.