Theorems · Theorem · group theory
AddSubgroup.mem_sup_of_normal_right
∀ {G : Type u_1} [inst : AddGroup G] {s t : AddSubgroup G} [ht : t.Normal] {x : G},
x ∈ s ⊔ t ↔ ∃ y ∈ s, ∃ z ∈ t, y + z = x- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- add_assocproof · cited by 746
- neg_add_revproof · cited by 236
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.closureproof · cited by 156
- neg_add_cancel_leftproof · cited by 84
- add_neg_cancel_leftproof · cited by 76
- AddSubgroup.zero_memproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_sup_of_normal_leftproof · cited by 1