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Theorems · Theorem · commutative algebra

Subsemiring.mem_map

∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] {f : R →+* S} {s : Subsemiring R}
  {y : S}, y ∈ Subsemiring.map f s ↔ ∃ x ∈ s, f x = y
Defined in
Mathlib.Algebra.Ring.Subsemiring.Basic
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses no axioms
Assumes
NonAssocSemiringNonAssocSemiring
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Around this declaration

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

Subalgebra.mem_map · cited by 4Subalgebra.mem_mapStarSubalgebra.mem_map · cited by 0StarSubalgebra.mem_mapDFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomNonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringSubsemiring.map · cited by 29Subsemiring.mapSubsemiring.mem_mapCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.