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Theorems · Definition · group theory

AddSubmonoid.copy

{M : Type u_1} → [inst : AddZeroClass M] → (S : AddSubmonoid M) → (s : Set M) → s = ↑S → AddSubmonoid M

Copy an additive submonoid replacing carrier with a set that is equal to it.

Defined in
Mathlib.Algebra.Group.Submonoid.Defs
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddZeroClass
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Around this declaration

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

AddMonoidHom.mrange · cited by 61AddMonoidHom.mrangeAddSubmonoid.multiples · cited by 40AddSubmonoid.multiplesSubsemiring.copy · cited by 5Subsemiring.copyNonUnitalSubsemiring.copy · cited by 4NonUnitalSubsemiring.copySubmodule.coe_iSup_of_directed · cited by 3Submodule.coe_iSup_of_dir…AddSubmonoid.copy_eq · cited by 1AddSubmonoid.copy_eqAddSubmonoid.coe_copy · cited by 0AddSubmonoid.coe_copySet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.copyCITED BYCITES

Cites4

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

Cited by7

Results whose statement or proof uses this declaration.