Theorems · Theorem · group theory
Submonoid.eq_bot_iff_forall
∀ {M : Type u_1} [inst : MulOneClass M] (S : Submonoid M), S = ⊥ ↔ ∀ x ∈ S, x = 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- SetLike.ext_iffproof · cited by 64
- Submonoid.one_memproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.eq_bot_iff_forallproof · cited by 7
- Submonoid.eq_bot_of_subsingletonproof · cited by 1
- Submonoid.card_le_one_iff_eq_botproof · cited by 0