Theorems · Theorem · group theory
Subgroup.mem_sup_of_normal_right
∀ {G : Type u_1} [inst : Group G] {s t : Subgroup 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
- GroupSubgroup.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
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- Subgroup.Normalstatement and proof · cited by 334
- mul_inv_revproof · cited by 270
- Subgroup.closureproof · cited by 196
- inv_mul_cancel_leftproof · cited by 88
- mul_inv_cancel_leftproof · cited by 86
- Subgroup.inv_memproof · cited by 40
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.mem_sup_of_normal_leftproof · cited by 1