Theorems · Theorem · ring theory
NonUnitalSubsemiring.subset_closure
∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] {s : Set R}, s ⊆ ↑(NonUnitalSubsemiring.closure s)The non-unital subsemiring generated by a set includes the set.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SetLike.coestatement and proof · cited by 8,199
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalSubsemiringstatement and proof · cited by 201
- NonUnitalSubsemiring.closurestatement · cited by 31
- NonUnitalSubsemiring.mem_closureproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- NonUnitalAlgebra.subset_adjoinproof · cited by 13
- NonUnitalSubsemiring.closure_leproof · cited by 8
- NonUnitalAlgebra.gcproof · cited by 5
- NonUnitalSubsemiring.closure_monoproof · cited by 2
- NonUnitalSubsemiring.mem_closure_of_memproof · cited by 1
- NonUnitalSubsemiring.closure_inductionstatement and proof · cited by 1
- NonUnitalSubsemiring.closure_subsemigroup_closureproof · cited by 1
- NonUnitalRingHom.sclosure_preimage_leproof · cited by 0
- NonUnitalSubsemiring.closure_induction₂statement and proof · cited by 0
- NonUnitalSubsemiring.notMem_of_notMem_closureproof · cited by 0