Theorems · Theorem · group theory
AddGroup.rank_spec
∀ (G : Type u_1) [inst : AddGroup G] [h : AddGroup.FG G], ∃ S, S.card = AddGroup.rank G ∧ AddSubgroup.closure ↑S = ⊤
- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Finset.cardstatement · cited by 2,327
- AddSubgroup.closurestatement · cited by 156
- Nat.find_specproof · cited by 74
- AddGroup.FGstatement and proof · cited by 37
- AddGroup.rankstatement · cited by 14
- AddGroup.fg_iff'proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddGroup.rank_le_of_surjectiveproof · cited by 3
- AddGroup.rank_eq_zero_iffproof · cited by 2
- card_dvd_exponent_nsmul_rankproof · cited by 1