Theorems · Theorem · group theory
AddSubgroup.mem_sup
∀ {C : Type u_2} [inst : AddCommGroup C] {s t : AddSubgroup C} {x : C}, x ∈ s ⊔ t ↔ ∃ y ∈ s, ∃ z ∈ t, y + z = x- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- AddSubgroupstatement and proof · cited by 3,232
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- neg_add_revproof · cited by 236
- AddMemClass.add_memproof · cited by 229
- AddSubgroup.closureproof · cited by 156
- add_left_commproof · cited by 76
- NegMemClass.neg_memproof · cited by 63
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_closure_pairproof · cited by 0
- Submodule.sup_toAddSubgroupproof · cited by 0
- AddSubgroup.mem_sup'proof · cited by 0
- AddSubgroup.exists_mem_supproof · cited by 0