Theorems · Theorem · group theory
AddGroup.rank_pos
∀ (G : Type u_1) [inst : AddGroup G] [Nontrivial G] [inst_2 : AddGroup.FG G], 0 < AddGroup.rank G
- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Nontrivialstatement and proof · cited by 2,416
- pos_iff_ne_zeroproof · cited by 180
- AddGroup.FGstatement and proof · cited by 37
- not_subsingleton_iff_nontrivialproof · cited by 21
- AddGroup.rankstatement and proof · cited by 14
- AddGroup.rank_eq_zero_iffproof · cited by 2
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