Theorems · Theorem · group theory
AddSubgroup.closure_le_centralizer_centralizer
∀ {G : Type u_1} [inst : AddGroup G] (s : Set G),
AddSubgroup.closure s ≤ AddSubgroup.centralizer ↑(AddSubgroup.centralizer s)- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.closurestatement · cited by 156
- AddSubgroup.closure_leproof · cited by 30
- AddSubgroup.centralizerstatement and proof · cited by 24
- Set.subset_addCentralizer_addCentralizerproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.centralizer_closureproof · cited by 1
- AddSubgroup.isAddCommutative_closureproof · cited by 0