Theorems · Theorem · commutative algebra
Subring.mem_map_equiv
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R ≃+* S} {K : Subring R} {x : S},
x ∈ Subring.map (↑f) K ↔ f.symm x ∈ K- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingEquivstatement and proof · cited by 1,147
- RingHomClass.toRingHomstatement · cited by 746
- Subringstatement and proof · cited by 602
- RingEquiv.symmstatement · cited by 567
- NonAssocRingstatement and proof · cited by 483
- Subring.mapstatement · cited by 33
- Set.mem_image_equivproof · cited by 22
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