Theorems · Definition · group theory
Submonoid.gi
(M : Type u_1) → [inst : MulOneClass M] → GaloisInsertion Submonoid.closure SetLike.coe
closure forms a Galois insertion with the coercion to set.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
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 and proof · cited by 8,199
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.closurestatement and proof · cited by 167
- GaloisInsertionstatement · cited by 35
- Submonoid.closure_leproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- Submonoid.closure_eqproof · cited by 13
- Submonoid.closure_unionproof · cited by 10
- MonoidHom.map_mclosureproof · cited by 10
- Submonoid.closure_iUnionproof · cited by 5
- Submonoid.closure_emptyproof · cited by 1