Theorems · Theorem · group theory
AddSubmonoid.eq_bot_iff_forall
∀ {M : Type u_1} [inst : AddZeroClass M] (S : AddSubmonoid M), S = ⊥ ↔ ∀ x ∈ S, x = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- SetLike.ext_iffproof · cited by 64
- AddSubmonoid.zero_memproof · cited by 17
- AddSubmonoid.mem_botproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.eq_bot_iff_forallproof · cited by 11
- AddSubmonoid.bot_or_nontrivialproof · cited by 1
- AddSubmonoid.eq_bot_of_subsingletonproof · cited by 1
- AddSubmonoid.card_le_one_iff_eq_botproof · cited by 0