Theorems · Theorem · group theory
AddSubgroup.closure_eq_of_le
∀ {G : Type u_1} [inst : AddGroup G] (K : AddSubgroup G) {k : Set G},
k ⊆ ↑K → K ≤ AddSubgroup.closure k → AddSubgroup.closure k = K- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 1 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.
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_antisymmproof · cited by 2,068
- AddSubgroup.closurestatement and proof · cited by 156
- AddSubgroup.closure_leproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.span_int_eq_addSubgroupClosureproof · cited by 5