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Theorems · Theorem · group theory

AddSubsemigroup.le_prod_iff

∀ {M : Type u_1} {N : Type u_2} [inst : Add M] [inst_1 : Add N] {s : AddSubsemigroup M} {t : AddSubsemigroup N}
  {u : AddSubsemigroup (M × N)},
  u ≤ s.prod t ↔ AddSubsemigroup.map (AddHom.fst M N) u ≤ s ∧ AddSubsemigroup.map (AddHom.snd M N) u ≤ t
Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
AddAdd
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AddSubsemigroup.prod_eq_top_iff · cited by 0AddSubsemigroup.prod_eq_t…DFunLike.coe · cited by 62936DFunLike.coeSetLike.coe · cited by 8199SetLike.coeAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.map · cited by 50AddSubsemigroup.mapAddSubsemigroup.prod · cited by 11AddSubsemigroup.prodAddHom.snd · cited by 9AddHom.sndAddHom.fst · cited by 8AddHom.fstAddSubsemigroup.le_prod_iffCITED BYCITES

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