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Theorems · Theorem · group theory

isCyclic_left_of_prod

∀ (M : Type u_4) (N : Type u_5) [inst : Group M] [inst_1 : Group N] [cyc : IsCyclic (M × N)], IsCyclic M
Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
GroupGroupIsCyclic
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Group.isCyclic_prod_iff · cited by 2Group.isCyclic_prod_iffcoprime_card_of_isCyclic_prod · cited by 1coprime_card_of_isCyclic_…Group · cited by 6238GroupIsCyclic · cited by 122IsCyclicMonoidHom.fst · cited by 28MonoidHom.fstProd.fst_surjective · cited by 22Prod.fst_surjectiveisCyclic_of_surjective · cited by 14isCyclic_of_surjectiveisCyclic_left_of_prodCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.