Theorems · Theorem · ring theory
NonUnitalSubsemiring.coe_iSup_of_directed
∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] {ι : Sort u_2} [hι : Nonempty ι] {S : ι → NonUnitalSubsemiring R},
Directed (fun x1 x2 => x1 ≤ x2) S → ↑(⨆ i, S i) = ⋃ i, ↑(S i)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 8,199
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Set.extproof · cited by 2,266
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Directedstatement and proof · cited by 213
- NonUnitalSubsemiringstatement and proof · cited by 201
- NonUnitalSubsemiring.mem_iSup_of_directedproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.isMulCommutative_iSupproof · cited by 3
- NonUnitalSubalgebra.coe_iSup_of_directedproof · cited by 2
- NonUnitalSubalgebra.isMulCommutative_iSupproof · cited by 0
- NonUnitalSubring.isMulCommutative_iSupproof · cited by 0
- NonUnitalStarSubalgebra.isMulCommutative_iSupproof · cited by 0