Theorems · Theorem · commutative algebra
Subring.mem_map
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S} {s : Subring R} {y : S},
y ∈ Subring.map f s ↔ ∃ x ∈ s, f x = y- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subring.mapstatement · cited by 33
Cited by5
Results whose statement or proof uses this declaration.
- Subring.mem_closure_image_ofproof · cited by 1
- Subring.comap_map_eqproof · cited by 1
- LaurentSeries.powerSeriesEquivSubring_applystatement · cited by 0
- IsDiscreteValuationRing.map_algebraMap_eq_valuationSubringproof · cited by 0
- NumberField.canonicalEmbedding.mem_span_latticeBasisproof · cited by 0