Theorems · Theorem · group theory
AddSubgroup.zmultiples_eq_bot
∀ {G : Type u_1} [inst : AddGroup G] {g : G}, AddSubgroup.zmultiples g = ⊥ ↔ g = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 74 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
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement · cited by 493
- eq_bot_iffproof · cited by 159
- AddSubgroup.mem_botproof · cited by 18
- AddSubgroup.zmultiples_leproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.zmultiples_ne_botproof · cited by 3
- AddSubgroup.zmultiples_zero_eq_botproof · cited by 2
- IsSimpleAddGroup.prime_cardproof · cited by 2
- zmultiples_eq_top_of_prime_cardproof · cited by 1
- ZMod.minOrderproof · cited by 1