Theorems · Theorem · commutative algebra
Subring.map_iInf
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {ι : Sort u_1} [Nonempty ι] (f : R →+* S),
Function.Injective ⇑f → ∀ (s : ι → Subring R), Subring.map f (iInf s) = ⨅ i, Subring.map f (s i)- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Set.imageproof · cited by 5,609
- iInfstatement and proof · cited by 1,690
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- SetLike.coe_injectiveproof · cited by 374
- Subring.mapstatement and proof · cited by 33
- Set.injOn_of_injectiveproof · cited by 28
- Set.InjOn.image_iInter_eqproof · cited by 22
- Subring.coe_iInfproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.