Theorems · Definition · ring theory
Subring.mopRingEquivOp
{R : Type u_2} → [inst : NonAssocRing R] → (S : Subring R) → (↥S)ᵐᵒᵖ ≃+* ↥S.opBijection between MulOpposite of a subring S and its opposite.
- Defined in
- Mathlib.Algebra.Ring.Subring.MulOpposite
- Cited by
- 2 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingEquivstatement · cited by 1,147
- MulOppositestatement · cited by 1,135
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subring.toSubsemiringproof · cited by 71
- Subring.opstatement · cited by 32
- Subsemiring.mopRingEquivOpproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subring.mopRingEquivOp_symm_applystatement and proof · cited by 0
- Subring.mopRingEquivOp_apply_coestatement and proof · cited by 0