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Theorems · Theorem · commutative algebra

Subsemiring.closure_sUnion

∀ {R : Type u} [inst : NonAssocSemiring R] (s : Set (Set R)),
  Subsemiring.closure (⋃₀ s) = ⨆ t ∈ s, Subsemiring.closure t
Defined in
Mathlib.Algebra.Ring.Subsemiring.Basic
Cited by
1 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonAssocSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.sSup_toSubsemiring · cited by 1Algebra.sSup_toSubsemiringSet · cited by 53352SetiSup · cited by 2415iSupNonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringSet.sUnion · cited by 392Set.sUnionGaloisInsertion.gc · cited by 137GaloisInsertion.gcSubsemiring.closure · cited by 53Subsemiring.closureGaloisConnection.l_sSup · cited by 19GaloisConnection.l_sSupSubsemiring.gi · cited by 6Subsemiring.giSubsemiring.closure_sUnionCITED BYCITES

Cites9

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Cited by1

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