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Theorems · Theorem · group theory

AddSubsemigroup.comap_sup_map_of_injective

∀ {M : Type u_1} {N : Type u_2} [inst : Add M] [inst_1 : Add N] {f : M →ₙ+ N},
  Function.Injective ⇑f →
    ∀ (S T : AddSubsemigroup M), AddSubsemigroup.comap f (AddSubsemigroup.map f S ⊔ AddSubsemigroup.map f T) = S ⊔ T
Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
0 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddAdd
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DFunLike.coe · cited by 62936DFunLike.coeAddHom · cited by 294AddHomAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.map · cited by 50AddSubsemigroup.mapAddSubsemigroup.comap · cited by 39AddSubsemigroup.comapAddSubsemigroup.gciMapComap · cited by 9AddSubsemigroup.gciMapCom…GaloisCoinsertion.u_sup_l · cited by 9GaloisCoinsertion.u_sup_lAddSubsemigroup.comap_sup_map…CITED BYCITES

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