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Theorems · Theorem · group theory

Subgroup.div_mem

∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) {x y : G}, x ∈ H → y ∈ H → x / y ∈ H

A subgroup is closed under division.

Defined in
Mathlib.Algebra.Group.Subgroup.Defs
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
Group

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Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Groupstatement and proof · cited by 6,238
  • Subgroupstatement and proof · cited by 3,593
  • div_memproof · cited by 9

Cited by1

Results whose statement or proof uses this declaration.