Theorems · Theorem · group theory
AddSubmonoid.pi_eq_bot_iff
∀ {ι : Type u_4} {M : ι → Type u_5} [inst : (i : ι) → AddZeroClass (M i)] (S : (i : ι) → AddSubmonoid (M i)),
AddSubmonoid.pi Set.univ S = ⊥ ↔ ∀ (i : ι), S i = ⊥- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
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
- Set.univstatement · cited by 3,945
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- SetLike.ext'_iffproof · cited by 78
- AddSubmonoid.pistatement · cited by 20
- Set.univ_pi_eq_singleton_iffproof · cited by 4
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Results whose statement or proof uses this declaration.
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