Theorems · Theorem · group theory
AddSubgroup.exists_mem_sup
∀ {C : Type u_2} [inst : AddCommGroup C] {s t : AddSubgroup C} {P : C → Prop},
(∃ x ∈ s ⊔ t, P x) ↔ ∃ x₁ ∈ s, ∃ x₂ ∈ t, P (x₁ + x₂)- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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Cites4
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
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.mem_supproof · cited by 4
- exists_exists_and_exists_and_eq_andproof · cited by 2
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