Theorems · Theorem · group theory
infinite_zmultiples
∀ {α : Type u_3} [inst : AddGroup α] {a : α}, (↑(AddSubgroup.zmultiples a)).Infinite ↔ ¬IsOfFinAddOrder a- Defined in
- Mathlib.Data.ZMod.QuotientGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement · cited by 493
- Iff.notproof · cited by 489
- Set.Infinitestatement · cited by 263
- IsOfFinAddOrderstatement · cited by 105
- finite_zmultiplesproof · cited by 3
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