Theorems · Theorem · commutative algebra
Subring.closure_sUnion
∀ {R : Type u} [inst : NonAssocRing R] (s : Set (Set R)), Subring.closure (⋃₀ s) = ⨆ t ∈ s, Subring.closure t- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- iSupstatement · cited by 2,415
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Set.sUnionstatement · cited by 392
- GaloisInsertion.gcproof · cited by 137
- Subring.closurestatement · cited by 78
- GaloisConnection.l_sSupproof · cited by 19
- Subring.giproof · cited by 6
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