Theorems · Theorem · ring theory
Subsemigroup.nonUnitalSubsemiringClosure_eq_closure
∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] (M : Subsemigroup R),
M.nonUnitalSubsemiringClosure = NonUnitalSubsemiring.closure ↑MThe NonUnitalSubsemiring generated by a multiplicative subsemigroup coincides with the
NonUnitalSubsemiring.closure of the subsemigroup itself .
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- AddSubmonoidproof · cited by 1,178
- Set.iInterproof · cited by 1,084
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Subsemigroupstatement and proof · cited by 323
- NonUnitalSubsemiringstatement and proof · cited by 201
- NonUnitalSubsemiring.toAddSubmonoidproof · cited by 56
- NonUnitalSubsemiring.closurestatement and proof · cited by 31
- AddSubmonoid.mem_closureproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.coe_closure_eqproof · cited by 1
- NonUnitalSubsemiring.closure_isSquareproof · cited by 1