Theorems · Theorem · group theory
AddGroup.rank_eq_zero_iff
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : AddGroup.FG G], AddGroup.rank G = 0 ↔ Subsingleton G- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddGroup.FG
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- Finset.cardproof · cited by 2,327
- AddSubgroup.closureproof · cited by 156
- Finset.coe_emptyproof · cited by 109
- AddGroup.FGstatement and proof · cited by 37
- Finset.card_eq_zeroproof · cited by 34
- subsingleton_iff_bot_eq_topproof · cited by 16
- AddGroup.rankstatement and proof · cited by 14
- AddSubgroup.subsingleton_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddCommGroup.freeRank_eq_zero_iffproof · cited by 1
- AddGroup.rank_posproof · cited by 0