Theorems · Theorem · commutative algebra
Subring.mem_comap
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {s : Subring S} {f : R →+* S} {x : R},
x ∈ Subring.comap f s ↔ f x ∈ s- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 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.comapstatement · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Subring.comap_map_eqproof · cited by 1
- Subring.closure_preimage_leproof · cited by 0
- RingHom.closure_preimage_leproof · cited by 0