Theorems · Theorem · ring theory
Subring.op_le_iff
∀ {R : Type u_2} [inst : NonAssocRing R] {S₁ : Subring R} {S₂ : Subring Rᵐᵒᵖ}, S₁.op ≤ S₂ ↔ S₁ ≤ S₂.unop- 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
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulOppositestatement and proof · 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
- Subring.unopstatement · cited by 25
- MulOpposite.op_surjectiveproof · cited by 21
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