Theorems · Theorem · ring theory
NonUnitalSubring.subset_closure
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {s : Set R}, s ⊆ ↑(NonUnitalSubring.closure s)The NonUnitalSubring generated by a set includes the set.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 71 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.
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
- NonUnitalNonAssocRingstatement and proof · cited by 354
- NonUnitalSubringstatement and proof · cited by 185
- NonUnitalSubring.closurestatement · cited by 23
- NonUnitalSubring.mem_closureproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- NonUnitalSubring.closure_leproof · cited by 7
- NonUnitalSubring.closure_inductionstatement and proof · cited by 2
- NonUnitalSubring.closure_monoproof · cited by 0
- NonUnitalSubring.closure_preimage_leproof · cited by 0
- NonUnitalRingHom.closure_preimage_leproof · cited by 0
- NonUnitalSubring.notMem_of_notMem_closureproof · cited by 0
- NonUnitalSubring.mem_closure_iffproof · cited by 0
- NonUnitalSubring.mem_closure_of_memproof · cited by 0
- NonUnitalSubring.closure_induction₂statement and proof · cited by 0