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Theorems · Theorem · group theory

Subsemigroup.comap_sup_map_of_injective

∀ {M : Type u_1} {N : Type u_2} [inst : Mul M] [inst_1 : Mul N] {f : M →ₙ* N},
  Function.Injective ⇑f →
    ∀ (S T : Subsemigroup M), Subsemigroup.comap f (Subsemigroup.map f S ⊔ Subsemigroup.map f T) = S ⊔ T
Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
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0 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulMul
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DFunLike.coe · cited by 62936DFunLike.coeSubsemigroup · cited by 323SubsemigroupMulHom · cited by 299MulHomSubsemigroup.map · cited by 51Subsemigroup.mapSubsemigroup.comap · cited by 39Subsemigroup.comapGaloisCoinsertion.u_sup_l · cited by 9GaloisCoinsertion.u_sup_lSubsemigroup.gciMapComap · cited by 9Subsemigroup.gciMapComapSubsemigroup.comap_sup_map_of…CITED BYCITES

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