Theorems · Theorem · group theory
AddSubmonoid.mem_sup
∀ {N : Type u_4} [inst : AddCommMonoid N] {s t : AddSubmonoid N} {x : N}, x ∈ s ⊔ t ↔ ∃ y ∈ s, ∃ z ∈ t, y + z = x- Cited by
- 8 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoidHom.mem_mrangeproof · cited by 10
- AddSubmonoid.sup_eq_rangeproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- AddSubmonoid.coe_supproof · cited by 2
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Submodule.sup_toAddSubmonoidproof · cited by 1
- Algebra.FinitePresentation.ker_fg_of_mvPolynomialproof · cited by 1
- AddSubmonoid.exists_mem_supproof · cited by 0
- AddSubmonoid.sup_mulproof · cited by 0
- AddSubmonoid.forall_mem_supproof · cited by 0
- AddSubmonoid.mem_closure_pairproof · cited by 0