Theorems · Theorem · group theory
Subgroup.disjoint_iff_mul_eq_one
∀ {G : Type u_1} [inst : Group G] {H₁ H₂ : Subgroup G},
Disjoint H₁ H₂ ↔ ∀ {x y : G}, x ∈ H₁ → y ∈ H₂ → x * y = 1 → x = 1 ∧ y = 1- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- Disjointstatement · cited by 2,201
- Subgroup.inv_memproof · cited by 40
- mul_inv_eq_oneproof · cited by 20
- eq_inv_iff_mul_eq_oneproof · cited by 5
- Subgroup.disjoint_def'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.mul_injective_of_disjointproof · cited by 2
- Subgroup.eq_one_of_noncommProd_eq_one_of_iSupIndepproof · cited by 1