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Theorems · Theorem · group theory

AddSubmonoid.mem_comap

∀ {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] {S : AddSubmonoid N} {f : F} {x : M},
  x ∈ AddSubmonoid.comap f S ↔ f x ∈ S
Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
8 results in Mathlib
Foundations
Depth 16 from the axioms · uses no axioms
Assumes
AddZeroClassAddZeroClassFunLikeAddMonoidHomClass
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Around this declaration

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

AddSubmonoid.top_prod · cited by 2AddSubmonoid.top_prodAddSubmonoid.prod_top · cited by 1AddSubmonoid.prod_topAddMonoidHom.mclosure_preimage_le · cited by 1AddMonoidHom.mclosure_pre…AddMonoidHom.addSubmonoidComap_surjective_of_surjective · cited by 1AddMonoidHom.addSubmonoid…AddSubmonoid.closure_mul_closure · cited by 1AddSubmonoid.closure_mul_…AddSubmonoid.le_comap_single_pi · cited by 1AddSubmonoid.le_comap_sin…AddSubmonoid.subPairs_comap · cited by 0AddSubmonoid.subPairs_com…AddSubmonoid.comap_id · cited by 0AddSubmonoid.comap_idDFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddMonoidHomClass · cited by 252AddMonoidHomClassAddSubmonoid.comap · cited by 62AddSubmonoid.comapAddSubmonoid.mem_comapCITED BYCITES

Cites6

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

Cited by8

Results whose statement or proof uses this declaration.