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Theorems · Definition · group theory

Submonoid.unop

{M : Type u_2} → [inst : MulOneClass M] → Submonoid Mᵐᵒᵖ → Submonoid M

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

Defined in
Mathlib.Algebra.Group.Submonoid.MulOpposite
Cited by
26 results in Mathlib
Foundations
Depth 20 from the axioms · uses Quot.sound
Assumes
MulOneClass
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Around this declaration

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

Subsemiring.unop · cited by 26Subsemiring.unopSubmonoid.opEquiv · cited by 18Submonoid.opEquivSubmonoid.unop_injective · cited by 2Submonoid.unop_injectiveSubmonoid.coe_unop · cited by 1Submonoid.coe_unopSubmonoid.op_sInf · cited by 1Submonoid.op_sInfSubmonoid.op_unop · cited by 1Submonoid.op_unopSubmonoid.unop_bot · cited by 1Submonoid.unop_botSubmonoid.unop_top · cited by 1Submonoid.unop_topSubgroup.unop_toSubmonoid · cited by 0Subgroup.unop_toSubmonoidSubsemiring.unop_toSubmonoid · cited by 0Subsemiring.unop_toSubmon…Submonoid.opEquiv_symm_apply · cited by 0Submonoid.opEquiv_symm_ap…Submonoid.op_le_iff · cited by 0Submonoid.op_le_iffSubmonoid.mem_unop · cited by 0Submonoid.mem_unopSubmonoid.op_sSup · cited by 0Submonoid.op_sSupSubmonoid.le_op_iff · cited by 0Submonoid.le_op_iffSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageSubmonoid · cited by 3086SubmonoidMulOpposite · cited by 1135MulOppositeMulOneClass · cited by 1018MulOneClassMulOpposite.op · cited by 520MulOpposite.opSubmonoid.unopCITED BYCITES

Cites6

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

Cited by28

Results whose statement or proof uses this declaration.