Theorems · Definition · group theory
AddSubsemigroup.gi
(M : Type u_1) → [inst : Add M] → GaloisInsertion AddSubsemigroup.closure SetLike.coe
closure forms a Galois insertion with the coercion to set.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- AddSubsemigroupstatement and proof · cited by 262
- GaloisInsertionstatement · cited by 35
- AddSubsemigroup.closurestatement · cited by 34
- AddSubsemigroup.closure_leproof · cited by 11
- GaloisConnection.toGaloisInsertionproof · cited by 0
Cited by5
Results whose statement or proof uses this declaration.
- AddSubsemigroup.closure_eqproof · cited by 3
- AddSubsemigroup.closure_iUnionproof · cited by 2
- AddSubsemigroup.closure_unionproof · cited by 0
- AddSubsemigroup.closure_emptyproof · cited by 0
- AddHom.map_mclosureproof · cited by 0