Theorems · Theorem · group theory
AddCommGroup.freeRank_eq_zero
∀ {G : Type u_1} [inst : AddCommGroup G], IsAddTorsion G → ∀ [inst_1 : AddGroup.FG G], AddCommGroup.freeRank G = 0- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupAddGroup.FG
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.
- AddCommGroupstatement and proof · cited by 12,871
- IsAddTorsionstatement and proof · cited by 42
- AddGroup.FGstatement and proof · cited by 37
- AddCommGroup.freeRankstatement · cited by 6
- AddCommGroup.freeRank_eq_zero_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddCommGroup.freeRank_eq_zero_of_finiteproof · cited by 0