Theorems · Theorem · group theory
AddSubgroupClass.subset_union
∀ {G : Type u_1} [inst : AddGroup G] {S : Type u_4} [inst_1 : SetLike S G] [AddSubgroupClass S G] [inst : LE S]
[IsConcreteLE S G] {H K L : S}, ↑H ⊆ ↑K ∪ ↑L ↔ H ≤ K ∨ H ≤ L- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- SetLikestatement and proof · cited by 1,084
- AddSubgroupClassstatement and proof · cited by 240
- AddMemClass.add_memproof · cited by 229
- SetLike.coe_subset_coeproof · cited by 53
- IsConcreteLEstatement and proof · cited by 28
- add_mem_cancel_rightproof · cited by 10
- SetLike.not_le_iff_existsproof · cited by 10
- mem_of_le_of_memproof · cited by 9
- add_mem_cancel_leftproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.subset_unionproof · cited by 1