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Theorems · Theorem · group theory

AddSubgroup.prod_le_iff

∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {H : AddSubgroup G} {K : AddSubgroup N}
  {J : AddSubgroup (G × N)},
  H.prod K ≤ J ↔ AddSubgroup.map (AddMonoidHom.inl G N) H ≤ J ∧ AddSubgroup.map (AddMonoidHom.inr G N) K ≤ J
Defined in
Mathlib.Algebra.Group.Subgroup.Basic
Cited by
2 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddGroup
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Around this declaration

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

AddSubgroup.addCommutator_sum_sum · cited by 1AddSubgroup.addCommutator…AddSubgroup.closure_prod · cited by 0AddSubgroup.closure_prodAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddSubgroup.map · cited by 189AddSubgroup.mapAddSubgroup.prod · cited by 34AddSubgroup.prodAddMonoidHom.inl · cited by 29AddMonoidHom.inlAddMonoidHom.inr · cited by 29AddMonoidHom.inrAddSubmonoid.prod_le_iff · cited by 5AddSubmonoid.prod_le_iffAddSubgroup.toAddSubmonoid_le · cited by 4AddSubgroup.toAddSubmonoi…AddSubgroup.prod_le_iffCITED BYCITES

Cites8

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Cited by2

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