Theorems · Theorem · ring theory
NonUnitalSubring.closure_le
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {s : Set R} {t : NonUnitalSubring R},
NonUnitalSubring.closure s ≤ t ↔ s ⊆ ↑tA NonUnitalSubring t includes closure s if and only if it includes s.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocRing
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.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- NonUnitalNonAssocRingstatement and proof · cited by 354
- Set.Subset.transproof · cited by 218
- NonUnitalSubringstatement and proof · cited by 185
- sInf_leproof · cited by 110
- NonUnitalSubring.closurestatement · cited by 23
- NonUnitalSubring.subset_closureproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- NonUnitalSubring.giproof · cited by 6
- NonUnitalSubring.closure_inductionproof · cited by 2
- NonUnitalSubring.closure_le_centralizer_centralizerproof · cited by 1
- NonUnitalRingHom.eqOn_set_closureproof · cited by 1
- NonUnitalSubring.closure_monoproof · cited by 0
- NonUnitalSubring.closure_preimage_leproof · cited by 0
- NonUnitalRingHom.closure_preimage_leproof · cited by 0
- NonUnitalSubring.closure_eq_of_leproof · cited by 0