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Theorems · Definition · ring theory

Subsemiring.unop

{R : Type u_2} → [inst : NonAssocSemiring R] → Subsemiring Rᵐᵒᵖ → Subsemiring R

Pull an opposite subsemiring back to a subsemiring along MulOpposite.op

Defined in
Mathlib.Algebra.Ring.Subsemiring.MulOpposite
Cited by
26 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
NonAssocSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subring.unop · cited by 25Subring.unopSubalgebra.unop · cited by 21Subalgebra.unopSubsemiring.opEquiv · cited by 18Subsemiring.opEquivSubsemiring.unop_injective · cited by 2Subsemiring.unop_injectiveSubsemiring.unop_bot · cited by 1Subsemiring.unop_botSubsemiring.unop_closure · cited by 1Subsemiring.unop_closureSubsemiring.unop_top · cited by 1Subsemiring.unop_topSubalgebra.unop_toSubsemiring · cited by 1Subalgebra.unop_toSubsemi…Subsemiring.coe_unop · cited by 1Subsemiring.coe_unopSubsemiring.op_sInf · cited by 1Subsemiring.op_sInfSubsemiring.op_unop · cited by 1Subsemiring.op_unopSubsemiring.unop_eq_bot · cited by 0Subsemiring.unop_eq_botSubsemiring.unop_eq_top · cited by 0Subsemiring.unop_eq_topSubsemiring.mem_unop · cited by 0Subsemiring.mem_unopSubsemiring.unop_iInf · cited by 0Subsemiring.unop_iInfSubmonoid · cited by 3086SubmonoidMulOpposite · cited by 1135MulOppositeNonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringSubsemigroup.carrier · cited by 160Subsemigroup.carrierSubmonoid.toSubsemigroup · cited by 159Submonoid.toSubsemigroupSubsemiring.toSubmonoid · cited by 153Subsemiring.toSubmonoidSubmonoid.unop · cited by 26Submonoid.unopSubsemiring.unopCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by29

Results whose statement or proof uses this declaration.