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Theorems · Theorem · group theory

AddSubmonoid.le_prod_iff

∀ {N : Type u_2} [inst : AddZeroClass N] {M : Type u_5} [inst_1 : AddZeroClass M] {s : AddSubmonoid M}
  {t : AddSubmonoid N} {u : AddSubmonoid (M × N)},
  u ≤ s.prod t ↔ AddSubmonoid.map (AddMonoidHom.fst M N) u ≤ s ∧ AddSubmonoid.map (AddMonoidHom.snd M N) u ≤ t
Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
2 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
AddZeroClassAddZeroClass
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Around this declaration

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

AddSubgroup.le_prod_iff · cited by 1AddSubgroup.le_prod_iffAddSubmonoid.prod_eq_top_iff · cited by 0AddSubmonoid.prod_eq_top_…DFunLike.coe · cited by 62936DFunLike.coeSetLike.coe · cited by 8199SetLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.map · cited by 99AddSubmonoid.mapAddMonoidHom.snd · cited by 42AddMonoidHom.sndAddMonoidHom.fst · cited by 39AddMonoidHom.fstAddSubmonoid.prod · cited by 27AddSubmonoid.prodAddSubmonoid.le_prod_iffCITED BYCITES

Cites9

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Cited by2

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