Theorems · Theorem · group theory
SubgroupClass.subset_union
∀ {G : Type u_1} [inst : Group G] {S : Type u_4} [inst_1 : SetLike S G] [SubgroupClass 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
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Groupstatement and proof · cited by 6,238
- SetLikestatement and proof · cited by 1,084
- MulMemClass.mul_memproof · cited by 173
- SetLike.coe_subset_coeproof · cited by 53
- SubgroupClassstatement and proof · cited by 34
- IsConcreteLEstatement and proof · cited by 28
- mul_mem_cancel_rightproof · cited by 11
- mul_mem_cancel_leftproof · cited by 10
- SetLike.not_le_iff_existsproof · cited by 10
- mem_of_le_of_memproof · cited by 9
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