Theorems · Theorem · ring theory
NonUnitalSubsemiring.isMulCommutative_iSup
∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] {ι : Sort u_2} [Nonempty ι] {S : ι → NonUnitalSubsemiring R}
[hS : ∀ (i : ι), IsMulCommutative ↥(S i)], Directed (fun x1 x2 => x1 ≤ x2) S → IsMulCommutative ↥(⨆ i, S i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Directedstatement and proof · cited by 213
- NonUnitalSubsemiringstatement and proof · cited by 201
- IsMulCommutativestatement and proof · cited by 95
- IsMulCommutative.of_setLike_mul_commproof · cited by 16
- setLike_mul_commproof · cited by 6
- NonUnitalSubsemiring.coe_iSup_of_directedproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.isMulCommutative_iSupproof · cited by 0
- NonUnitalSubring.isMulCommutative_iSupproof · cited by 0
- NonUnitalStarSubalgebra.isMulCommutative_iSupproof · cited by 0