Theorems · Theorem · group theory
AddSubgroup.op_le_op_iff
∀ {G : Type u_2} [inst : AddGroup G] {S₁ S₂ : AddSubgroup G}, S₁.op ≤ S₂.op ↔ S₁ ≤ S₂- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddOppositestatement · cited by 452
- Function.Surjective.forallproof · cited by 214
- AddSubgroup.opstatement · cited by 57
- AddOpposite.op_surjectiveproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.opEquivproof · cited by 18