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Theorems · Theorem · group theory

AddSubsemigroup.map_le_iff_le_comap

∀ {M : Type u_1} {N : Type u_2} [inst : Add M] [inst_1 : Add N] {f : M →ₙ+ N} {S : AddSubsemigroup M}
  {T : AddSubsemigroup N}, AddSubsemigroup.map f S ≤ T ↔ S ≤ AddSubsemigroup.comap f 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.gc_map_comap · cited by 15AddSubsemigroup.gc_map_co…AddHom · cited by 294AddHomAddSubsemigroup · cited by 262AddSubsemigroupSet.image_subset_iff · cited by 203Set.image_subset_iffAddSubsemigroup.map · cited by 50AddSubsemigroup.mapAddSubsemigroup.comap · cited by 39AddSubsemigroup.comapAddSubsemigroup.map_le_iff_le…CITED BYCITES

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