Theorems · Theorem · group theory
AddSubgroup.disjoint_iff_add_eq_zero
∀ {G : Type u_1} [inst : AddGroup G] {H₁ H₂ : AddSubgroup G},
Disjoint H₁ H₂ ↔ ∀ {x y : G}, x ∈ H₁ → y ∈ H₂ → x + y = 0 → x = 0 ∧ y = 0- 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
- 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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- zero_addproof · cited by 2,366
- Disjointstatement · cited by 2,201
- eq_neg_iff_add_eq_zeroproof · cited by 32
- AddSubgroup.neg_memproof · cited by 23
- add_neg_eq_zeroproof · cited by 20
- AddSubgroup.disjoint_def'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_iSupIndepproof · cited by 1
- AddSubgroup.add_injective_of_disjointproof · cited by 0