Theorems · Theorem · group theory
Infinite.addOrderOf_eq_zero_of_forall_mem_zmultiples
∀ {α : Type u_1} [inst : AddGroup α] [Infinite α] {g : α}, (∀ (x : α), x ∈ AddSubgroup.zmultiples g) → addOrderOf g = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- Infinitestatement and proof · cited by 352
- addOrderOfstatement · cited by 208
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- addOrderOf_eq_card_of_forall_mem_zmultiplesproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsAddCyclic.exponent_eq_zero_of_infiniteproof · cited by 0