Theorems · Theorem · ring theory
Subring.op_le_op_iff
∀ {R : Type u_2} [inst : NonAssocRing R] {S₁ S₂ : Subring R}, S₁.op ≤ S₂.op ↔ S₁ ≤ S₂- Defined in
- Mathlib.Algebra.Ring.Subring.MulOpposite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRing
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.
- MulOppositestatement · cited by 1,135
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Function.Surjective.forallproof · cited by 214
- Subring.opstatement · cited by 32
- MulOpposite.op_surjectiveproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Subring.opEquivproof · cited by 18