Theorems · Definition · group theory
Subsemigroup.gi
(M : Type u_1) → [inst : Mul M] → GaloisInsertion Subsemigroup.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
- Mul
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
- Subsemigroupstatement and proof · cited by 323
- Subsemigroup.closurestatement · cited by 43
- GaloisInsertionstatement · cited by 35
- Subsemigroup.closure_leproof · cited by 13
- GaloisConnection.toGaloisInsertionproof · cited by 0
Cited by5
Results whose statement or proof uses this declaration.
- Subsemigroup.closure_eqproof · cited by 3
- Subsemigroup.closure_iUnionproof · cited by 2
- MulHom.map_mclosureproof · cited by 0
- Subsemigroup.closure_unionproof · cited by 0
- Subsemigroup.closure_emptyproof · cited by 0