Theorems · Theorem · commutative algebra
Subring.coe_iInf
∀ {R : Type u} [inst : NonAssocRing R] {ι : Sort u_1} {S : ι → Subring R}, ↑(⨅ i, S i) = ⋂ i, ↑(S i)- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- iInfstatement · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Set.biInter_rangeproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- Set.integer_eqproof · cited by 0
- Subring.map_iInfproof · cited by 0