Theorems · Theorem · group theory
AddSubgroup.pi_eq_bot_iff
∀ {η : Type u_7} {f : η → Type u_8} [inst : (i : η) → AddGroup (f i)] (H : (i : η) → AddSubgroup (f i)),
AddSubgroup.pi Set.univ H = ⊥ ↔ ∀ (i : η), H i = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement · cited by 3,945
- AddSubgroupstatement and proof · cited by 3,232
- SetLike.ext'_iffproof · cited by 78
- AddSubgroup.pistatement · cited by 26
- Set.univ_pi_eq_singleton_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddGroup.nilpotencyClass_piproof · cited by 0
- AddGroup.isNilpotent_pi_of_bounded_classproof · cited by 0