Theorems · Theorem · group theory
Subgroup.mem_sup
∀ {C : Type u_2} [inst : CommGroup C] {s t : Subgroup C} {x : C}, x ∈ s ⊔ t ↔ ∃ y ∈ s, ∃ z ∈ t, y * z = x- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- CommGroupstatement and proof · cited by 990
- mul_inv_revproof · cited by 270
- Subgroup.closureproof · cited by 196
- mul_left_commproof · cited by 184
- MulMemClass.mul_memproof · cited by 173
- InvMemClass.inv_memproof · cited by 52
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.mem_closure_pairproof · cited by 0
- Subgroup.mem_sup'proof · cited by 0