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Theorems · Theorem · commutative algebra

Subsemiring.closure_union

∀ {R : Type u} [inst : NonAssocSemiring R] (s t : Set R),
  Subsemiring.closure (s ∪ t) = Subsemiring.closure s ⊔ Subsemiring.closure t
Defined in
Mathlib.Algebra.Ring.Subsemiring.Basic
Cited by
2 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.

Subsemiring.closure_insert_natCast · cited by 2Subsemiring.closure_inser…Algebra.sup_toSubsemiring · cited by 0Algebra.sup_toSubsemiringSet · cited by 53352SetNonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringGaloisInsertion.gc · cited by 137GaloisInsertion.gcGaloisConnection.l_sup · cited by 81GaloisConnection.l_supSubsemiring.closure · cited by 53Subsemiring.closureSubsemiring.gi · cited by 6Subsemiring.giSubsemiring.closure_unionCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.