Theorems · Theorem · group theory
not_isAddCyclic_prod_of_infinite_nontrivial
∀ (M : Type u_4) (N : Type u_5) [inst : AddGroup M] [inst_1 : AddGroup N] [Infinite M] [Nontrivial N], ¬IsAddCyclic (M × N)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomproof · cited by 3,230
- Finiteproof · cited by 3,029
- Nontrivialstatement and proof · cited by 2,416
- LT.lt.ne'proof · cited by 1,417
- ZModproof · cited by 1,024
- Nat.cardproof · cited by 844
- Infinitestatement and proof · cited by 352
- Nat.card_eq_fintype_cardproof · cited by 200
- AddMonoidHom.idproof · cited by 107
- dvd_zeroproof · cited by 63
Cited by2
Results whose statement or proof uses this declaration.
- not_isCyclic_prod_of_infinite_nontrivialproof · cited by 1
- AddGroup.isAddCyclic_prod_iffproof · cited by 0