Theorems · Definition · ring theory
Subsemiring.op
{R : Type u_2} → [inst : NonAssocSemiring R] → Subsemiring R → Subsemiring RᵐᵒᵖPull a subsemiring back to an opposite subsemiring along MulOpposite.unop
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidproof · cited by 3,086
- MulOppositestatement and proof · cited by 1,135
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
- Subsemiring.toSubmonoidproof · cited by 153
- Submonoid.opproof · cited by 38
Cited by52
Results whose statement or proof uses this declaration.
- Subring.opproof · cited by 32
- Subalgebra.opproof · cited by 30
- Subsemiring.opEquivproof · cited by 18
- Subsemiring.addEquivOpstatement and proof · cited by 8
- Subalgebra.linearEquivOpproof · cited by 3
- Subsemiring.ringEquivOpMopstatement and proof · cited by 2
- Subalgebra.mopAlgEquivOpproof · cited by 2
- Subalgebra.algEquivOpMopproof · cited by 2
- Subsemiring.mopRingEquivOpstatement and proof · cited by 2
- Subsemiring.op_closurestatement · cited by 2
- Subsemiring.op_injectivestatement · cited by 2
- Subsemiring.unop_closureproof · cited by 1