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Theorems · Theorem · group theory

AddSubmonoid.map_inl

∀ {N : Type u_2} [inst : AddZeroClass N] {M : Type u_5} [inst_1 : AddZeroClass M] (s : AddSubmonoid M),
  AddSubmonoid.map (AddMonoidHom.inl M N) s = s.prod ⊥
Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
AddZeroClassAddZeroClass
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Around this declaration

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

AddSubmonoid.mrange_inl · cited by 2AddSubmonoid.mrange_inlDFunLike.coe · cited by 62936DFunLike.coeSetLike.coe · cited by 8199SetLike.coeBot.bot · cited by 4720Bot.botAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidSet.mem_singleton · cited by 183Set.mem_singletonAddSubmonoid.map · cited by 99AddSubmonoid.mapAddSubmonoid.ext · cited by 32AddSubmonoid.extAddMonoidHom.inl · cited by 29AddMonoidHom.inlAddSubmonoid.prod · cited by 27AddSubmonoid.prodSet.eq_of_mem_singleton · cited by 22Set.eq_of_mem_singletonAddSubmonoid.map_inlCITED BYCITES

Cites12

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Cited by1

Results whose statement or proof uses this declaration.