Theorems · Theorem · group theory
AddSubgroup.IsSubnormal.iff_eq_top_or_exists
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G},
H.IsSubnormal ↔ H = ⊤ ∨ ∃ K, H < K ∧ K.IsSubnormal ∧ (H.addSubgroupOf K).Normal- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- LT.lt.leproof · cited by 2,189
- eq_or_neproof · cited by 1,117
- AddSubgroup.Normalstatement and proof · cited by 183
- Ne.lt_topproof · cited by 161
- LE.le.lt_of_neproof · cited by 116
- AddSubgroup.addSubgroupOfstatement and proof · cited by 87
- not_top_ltproof · cited by 17
- AddSubgroup.IsSubnormalstatement and proof · cited by 17
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