Theorems · Theorem · commutative algebra
Subring.one_mem
∀ {R : Type u} [inst : NonAssocRing R] (s : Subring R), 1 ∈ sA subring contains the ring's 1.
- Defined in
- Mathlib.Algebra.Ring.Subring.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- OneMemClass.one_memproof · cited by 87
Cited by5
Results whose statement or proof uses this declaration.
- FreeCommRing.isSupported_oneproof · cited by 2
- ValuationSubring.one_memproof · cited by 2
- Algebra.adjoin_eq_ring_closureproof · cited by 2
- Polynomial.toSubring_onestatement and proof · cited by 0
- Subring.toNonUnitalSubring_toSubringstatement and proof · cited by 0