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Theorems · Theorem · group theory

Subgroup.prod_le_iff

∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {H : Subgroup G} {K : Subgroup N}
  {J : Subgroup (G × N)}, H.prod K ≤ J ↔ Subgroup.map (MonoidHom.inl G N) H ≤ J ∧ Subgroup.map (MonoidHom.inr G N) K ≤ J
Defined in
Mathlib.Algebra.Group.Subgroup.Basic
Cited by
2 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
GroupGroup
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Around this declaration

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

Subgroup.commutator_prod_prod · cited by 1Subgroup.commutator_prod_…Subgroup.closure_prod · cited by 0Subgroup.closure_prodGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupSubgroup.map · cited by 301Subgroup.mapSubgroup.prod · cited by 35Subgroup.prodMonoidHom.inl · cited by 32MonoidHom.inlMonoidHom.inr · cited by 32MonoidHom.inrSubmonoid.prod_le_iff · cited by 4Submonoid.prod_le_iffSubgroup.prod_le_iffCITED BYCITES

Cites7

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Cited by2

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