Theorems · Theorem · ring theory
NonUnitalSubsemiring.closure_eq_of_le
∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] {s : Set R} {t : NonUnitalSubsemiring R},
s ⊆ ↑t → t ≤ NonUnitalSubsemiring.closure s → NonUnitalSubsemiring.closure s = t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
Cites7
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
- le_antisymmproof · cited by 2,068
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalSubsemiringstatement and proof · cited by 201
- NonUnitalSubsemiring.closurestatement and proof · cited by 31
- NonUnitalSubsemiring.closure_leproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.subsemiringClosure_toNonUnitalSubsemiringproof · cited by 1