Documentation Verification Report

MulOpposite

šŸ“ Source: Mathlib/RingTheory/Coalgebra/MulOpposite.lean

Statistics

MetricCount
DefinitionsMulOpposite, instCoalgebra, instCoalgebraStruct
3
Theoremscomul_def, counit_def
2
Total5

MulOpposite

Definitions

NameCategoryTheorems
instCoalgebra šŸ“–CompOp—
instCoalgebraStruct šŸ“–CompOp
2 mathmath: counit_def, comul_def

Theorems

NameKindAssumesProvesValidatesDepends On
comul_def šŸ“–mathematical—CoalgebraStruct.comul
MulOpposite
instAddCommMonoid
instModule
CommSemiring.toSemiring
instCoalgebraStruct
LinearMap.comp
TensorProduct
TensorProduct.addCommMonoid
TensorProduct.instModule
RingHom.id
Semiring.toNonAssocSemiring
RingHomCompTriple.ids
TensorProduct.map
LinearEquiv.toLinearMap
RingHomInvPair.ids
opLinearEquiv
LinearEquiv.symm
——
counit_def šŸ“–mathematical—CoalgebraStruct.counit
MulOpposite
instAddCommMonoid
instModule
CommSemiring.toSemiring
instCoalgebraStruct
LinearMap.comp
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
RingHom.id
RingHomCompTriple.ids
LinearEquiv.toLinearMap
RingHomInvPair.ids
LinearEquiv.symm
opLinearEquiv
——

(root)

Definitions

NameCategoryTheorems
MulOpposite šŸ“–CompOp
1085 mathmath: CliffordAlgebra.unop_reverseOp, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, DoubleCoset.doubleCoset_union_rightCoset, AddOpposite.instMulTorsionFree, HasStrictFDerivAt.fun_mul', CategoryTheory.preadditiveCoyonedaObj_map, MulOpposite.unop_zpow, AlgEquiv.moduleEndSelfOp_apply_apply, MulOpposite.continuousConstSMul, NormedGroup.to_isIsometricSMul_right, Finset.map_op_one, Subalgebra.op_toSubsemiring, MeasureTheory.Measure.IsMulRightInvariant.toSMulInvariantMeasure_op, Subring.coe_unop, Submonoid.le_op_iff, Language.reverseIso_apply, RingEquiv.toOpposite_symm_apply, Multiplicative.isIsIsometricVAdd'', MulOpposite.instMeasurableConstSMul, AlgEquiv.opOp_apply, Submonoid.equivOp_symm_apply_coe, Subgroup.unop_inf, MulOpposite.op_eq_one_iff, Finset.mul_subset_iff_right, LefttCancelMonoid.to_faithfulSMul_mulOpposite, hasStrictFDerivAt_list_prod_finRange', Matrix.isCentralScalar, TwoUniqueProds.instMulOpposite, TrivSqZeroExt.lift_inlAlgHom_inrHom, instRankConditionMulOpposite, Submonoid.op_iInf, Matrix.toLinearMapRight'_mul, MulOpposite.op_finsuppSum, MulOpposite.op_eq_zero_iff, Subalgebra.mem_op, mem_own_rightCoset, Subsemiring.op_injective, Submonoid.unop_eq_top, MulOpposite.op_ratCast, Finset.image_op_inv, RingEquiv.op_apply_apply, TrivSqZeroExt.snd_pow_eq_sum, ZeroAtInftyContinuousMap.instIsCentralScalar, MulEquiv.inv'_apply, Cardinal.mk_mulOpposite, TwoSidedIdeal.instSMulCommClassMulOppositeSubtypeMem, Polynomial.opRingEquiv_op_monomial, DoubleCentralizer.range_toProdMulOpposite, TrivSqZeroExt.isNilpotent_iff_isNilpotent_fst, Subgroup.instCountableSubtypeMulOppositeMemOp, Subgroup.equivOp_symm_apply_coe, RingEquiv.toOpposite_apply, Subring.addEquivOp_apply_coe, AlgEquiv.toOpposite_apply, Submonoid.unop_iInf, Subsemigroup.unop_iSup, Finset.op_smul_finset_mul_eq_mul_smul_finset, fderivWithin_fun_pow', Subsemigroup.centerToMulOpposite_apply_coe, MulOpposite.coe_opLinearEquiv_symm, Submodule.comap_op_mul, MeasurableSMul.op, Subalgebra.op_sSup, MulAction.right_quotientAction', Subgroup.op_le_op_iff, Finset.inv_smul_finset_distrib, TensorAlgebra.toTrivSqZeroExt_ι, Finset.doubling_lt_three_halves, LinearMap.ext_ring_op_iff, Subgroup.op_iSup, MulOpposite.instIsScalarTower, DoubleCentralizer.nnnorm_def', Subring.coe_op, AlgEquiv.toOpposite_symm_apply, MulHom.op_symm_apply_apply, Submonoid.unop_iSup, Prod.isCentralScalar, CompleteSpace.mulOpposite, Submodule.comap_op_pow, MulOpposite.opAddEquiv_apply, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, Subsemiring.op_eq_bot, TrivSqZeroExt.inv_inl, Subalgebra.op_sInf, Function.Embedding.instIsCentralScalar, MulOpposite.normOneClass, Subsemigroup.op_le_op_iff, Submonoid.unop_inf, IsScalarTower.opposite_mid, Subsemiring.op_eq_top, Subalgebra.op_bot, AlgEquiv.op_apply_apply, TrivSqZeroExt.inv_one, MulOpposite.instIsDomain, Submodule.LinearDisjoint.op, MulOpposite.nnnorm_unop, CategoryTheory.Mat.instFaithfulMat_SingleObjMulOppositeEquivalenceSingleObjInverse, MonoidAlgebra.opRingEquiv_single, CliffordAlgebra.op_reverse, RootPairing.range_weylGroup_coweightHom, Subsemiring.op_sup, Subgroup.op_bot, HasStrictFDerivAt.mul', isLinearTopology_iff_hasBasis_open_twoSidedIdeal, MulOpposite.instStarOrderedRing, Subgroup.op_iInf, Subgroup.unop_closure, MulOpposite.unop_sub, ExteriorAlgebra.toTrivSqZeroExt_comp_map, Finset.map_op_inv, Polynomial.leadingCoeff_opRingEquiv, MulOpposite.op_injective, Subsemigroup.opEquiv_symm_apply, Subgroup.unop_eq_bot, RingEquiv.mopMatrix_symm_apply, MulOpposite.instIsRightCancelMulZeroOfIsLeftCancelMulZero, TrivSqZeroExt.snd_list_prod, TrivSqZeroExt.fstHom_comp_map, Subring.op_le_op_iff, Finset.op_smul_finset_subset_mul, Subsemiring.op_le_op_iff, Subring.le_op_iff, measurable_mul_op, fderiv_fun_pow', RingEquiv.op_apply_symm_apply, MulAction.right_quotientAction, AlgHom.mulLeftRightMatrix.inv_comp, MulOpposite.instNontrivial, Subring.unop_injective, IsCentralScalar.unop_smul_eq_smul, MulOpposite.op_star, MulOpposite.norm_unop, MulOpposite.one_le_op, MulOpposite.map_op_nhds, Subsemiring.le_op_iff, Subsemigroup.equivOp_symm_apply_coe, MulOpposite.coe_opLinearEquiv_symm_addEquiv, TrivSqZeroExt.fst_exp, MulOpposite.instContinuousMul, TrivSqZeroExt.map_inr, MulOpposite.op_smul_eq_op_smul_op, RingHom.toOpposite_apply, RingEquiv.mopMatrix_apply, RingCon.unop_iff, Pi.isCentralScalar, Finset.inv_op_smul_finset_distrib, rightCoset_eq_iff, Subalgebra.unop_sup, MonoidAlgebra.opRingEquiv_symm_apply, AlgHom.op_apply_apply, AlgEquiv.toAlgHom_op, BoundedContinuousFunction.instIsCentralScalar, AlgEquiv.toLinearEquiv_toOpposite, Monoid.CoprodI.inv_def, Filter.isCentralScalar, DoubleCentralizer.toProdMulOpposite_injective, Subgroup.mem_op, MulEquiv.opOp_symm_apply, Matrix.op_smul_one_eq_diagonal, AddMonoidAlgebra.opRingEquiv_symm_single, DoubleCentralizer.norm_def', CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.full, CStarMatrix.norm_def', Subalgebra.LinearDisjoint.linearIndependent_left_op_of_flat, Subgroup.unop_normalizer, MulOpposite.instIsCancelMulZero, Module.Basis.mulOpposite_apply, AddMonoidAlgebra.opRingEquiv_symm_apply, FormalMultilinearSeries.ofScalarsSum_op, Matrix.toLinearEquivRight'OfInv_symm_apply, MulEquiv.op_apply_symm_apply, DualNumber.inv_eps, IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite, Subsemiring.op_sInf, Subsemiring.addEquivOp_apply_coe, IsRightRegular.op, IsBoundedSMul.op, NonUnitalSubsemiring.centerToMulOpposite_symm_apply_coe, HasStrictFDerivAt.list_prod', MulOpposite.op_mem_center_iff, MulAction.op_smul_set_stabilizer_subset, MulOpposite.uniformContinuousConstSMul, Module.Basis.mulOpposite_is_orthonormal_iff, AlgHom.toLinearMap_toOpposite, Subring.op_sup, Subring.mopRingEquivOp_apply_coe, MvPowerSeries.substAlgHom_eq_aeval, CategoryTheory.End.smul_left, TwoSidedIdeal.mem_op_iff, NormMulClass.toNormSMulClass_op, Subgroup.op_top, MulOpposite.edist_op, TrivSqZeroExt.fst_invOf, NormedAddGroupHom.isCentralScalar, MulOpposite.finrank, LeftCancelMonoid.to_faithfulSMul_mulOpposite, MulOpposite.unop_add, IsSimpleRing.instMulOpposite, Finset.smul_inv_mul_eq_inv_mul_opSMul, MulOpposite.exponent, MulOpposite.algebraMap_apply, MulOpposite.isCancelMulZero_iff, MulOpposite.instMeasurableMulā‚‚, RingEquiv.moduleEndSelf_symm_apply, op_smul_eq_mul, Matrix.transposeRingEquiv_symm_apply, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, Submonoid.op_eq_bot, Subring.op_injective, Matrix.vecMulVec_update, ZeroHom.instIsCentralScalar, Submodule.map_unop_mul, MulOpposite.op_zero, AdicCompletion.instIsCentralScalar, rank_lt_rank_dual', unop_map_list_prod, Polynomial.opRingEquiv_op_C, NonUnitalRingHom.fromOpposite_apply, Subalgebra.mopAlgEquivOp_symm_apply, MulOpposite.coe_opLinearEquiv_addEquiv, Subsemiring.unop_le_unop_iff, MulOpposite.instFree, Submonoid.centerToMulOpposite_apply_coe, summable_unop, Subalgebra.op_adjoin, AlgHom.opComm_symm_apply_apply, RingCon.op_iff, TrivSqZeroExt.map_comp_inlAlgHom, MulOpposite.commute_unop, Finset.image_op_one, Subsemiring.unop_closure, Subsemigroup.unop_eq_bot, fderiv_mul_const', MulOpposite.instIsCancelMul, AddMonoidHom.mulOp_apply_apply, TrivSqZeroExt.eq_smul_exp_of_ne_zero, OrthonormalBasis.toBasis_mulOpposite, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, TrivSqZeroExt.inl_mul_inr, Submonoid.op_sSup, Subgroup.smul_diff_smul', TrivSqZeroExt.fst_list_prod, Subgroup.centerToMulOpposite_apply_coe, MeasurableSMulā‚‚.op, RootPairing.Equiv.coweightHom_injective, LinearMap.instIsCentralScalar, Subsemiring.unop_eq_top, Submonoid.op_sInf, AlgEquiv.op_apply_symm_apply, SMulCommClass.op_left, Subalgebra.unop_top, MulOpposite.unop_neg, Set.isCentralScalar, TrivSqZeroExt.isNilpotent_inr, TwoSidedIdeal.opOrderIso_symm_apply, AlgEquiv.mopMatrix_apply, isUnit_op, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj, associator_op, MulOpposite.isometry_opLinearEquiv, MulOpposite.isLeftCancelAdd_iff, AlgHom.toRingHom_toOpposite, MeasureTheory.AEEqFun.instIsCentralScalar, Subgroup.Normal.of_unop, Subsemiring.op_iSup, Subalgebra.op_inf, Subgroup.op_inf, TrivSqZeroExt.mul_left_eq_one, Subalgebra.coe_op, MulOpposite.comap_unop_nhds, Subsemiring.opEquiv_apply, MulOpposite.isRightCancelMulZero_iff, Subring.unop_top, CStarRing.MulOpposite.instMulOpposite, CategoryTheory.Mat.instEssSurjMat_SingleObjMulOppositeEquivalenceSingleObjInverse, Subsemiring.op_closure, Subgroup.smul_opposite_image_mul_preimage, TrivSqZeroExt.snd_exp, MulOpposite.edist_unop, MulOpposite.unop_nnratCast, Subsemiring.unop_sup, RootPairing.Hom.coweightHom_injective, DualNumber.isNilpotent_iff_eps_dvd, TrivSqZeroExt.map_comp_inrHom, Subring.op_bot, Subgroup.normal_op, MulOpposite.inner_op, Subgroup.op_normalizer, MulOpposite.isRightCancelAdd_iff, fderiv_pow', MvPowerSeries.LinearTopology.instIsLinearTopologyMulOpposite, Semigroup.opposite_smulCommClass', Subsemigroup.mem_op, Subgroup.op_toSubsemigroup, MulOpposite.instIsUniformGroup, CategoryTheory.Mat.equivalenceSingleObjInverse_obj_carrier, Algebra.TensorProduct.opAlgEquiv_apply, IsIsometricSMul.opposite_of_comm, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.exists_d_comp_eq_d, AddHom.mulOp_apply_apply, lift_rank_lt_rank_dual', MulOpposite.unop_ratCast, UniqueMul.iff_mulOpposite, AlgHom.opComm_apply_apply, Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroupOp, Equiv.isCentralScalar, CategoryTheory.Abelian.full_comp_preadditiveCoyonedaObj, AddSubmonoid.pointwise_isCentralScalar, MulOpposite.unop_star, op_smul_coe_set, Subring.op_sSup, Subsemiring.op_le_iff, RingEquiv.moduleEndSelfOp_apply, Subsemiring.unop_sInf, MulOpposite.op_pow, IsAzumaya.mulLeftRight_comp_congr, TrivSqZeroExt.inr_mul_inr, Subalgebra.unop_bot, Subgroup.pointwise_isCentralScalar, MulOpposite.unop_smul, fderivWithin_fun_mul', Subsemiring.pointwise_central_scalar, MulOpposite.instLocallyCompactSpace, hasFDerivAt_list_prod', Matrix.toLinearMapRight'_mul_apply, Subring.centerToMulOpposite_symm_apply_coe, MulOpposite.instIsCancelAdd, AlgHom.mulLeftRight_apply, measurableSMul_opposite_of_mul, Subalgebra.linearEquivOp_apply_coe, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesInjectiveObjects, MulOpposite.coe_symm_opMulEquiv, IsAzumaya.bij, fderiv_mul', MulAction.Regular.isPretransitive_mulOpposite, Subsemigroup.op_iInf, Module.Basis.mulOpposite_repr_op, AlgEquiv.opComm_apply_apply, MulOpposite.op_smul, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, MulOpposite.opContinuousLinearEquiv_symm_apply, Subsemiring.mem_op, NonUnitalRingHom.op_symm_apply_apply, Subring.op_top, Submodule.map_unop_pow, Matrix.op_smul_eq_mul_diagonal, Con.orderIsoOp_symm_apply, Subring.mopRingEquivOp_symm_apply, instIsTorsionFreeMulOpposite, Polynomial.opRingEquiv_op_X, DualNumber.exists_mul_left_or_mul_right, Subsemiring.centerToMulOpposite_symm_apply_coe, MulOpposite.invariantBasisNumber_iff, MulOpposite.unop_pow, NormedSpace.exp_op, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, Submonoid.unop_top, MulOpposite.nndist_op, Subring.op_iInf, MonoidAlgebra.opRingEquiv_symm_single, hasSum_unop, hasFDerivWithinAt_pow', TrivSqZeroExt.isNilpotent_inl_iff, MulOpposite.unop_mul, Subalgebra.unop_toSubring, instIsTopologicalGroupMulOpposite, Subsemiring.addEquivOp_symm_apply_coe, Submonoid.op_iSup, Subgroup.properlyDiscontinuousSMul_opposite_of_tendsto_cofinite, TrivSqZeroExt.mul_inv_cancel, RingInvo.involution', AffineMap.isCentralScalar, Matrix.mul_single_eq_updateCol_zero, RingCon.opOrderIso_apply, RingEquiv.moduleEndSelf_apply, TrivSqZeroExt.inv_mul_cancel, Submonoid.coe_op, MulOpposite.continuous_unop, fderivWithin_mul_const', TwoSidedIdeal.opOrderIso_apply, instIsTopologicalRingMulOpposite, AddEquiv.mulOp_symm_apply, Subsemiring.centerToMulOpposite_apply_coe, hasFDerivAt_list_prod_finRange', Subsemigroup.unop_sup, Submodule.equivOpposite_apply, Sum.instIsCentralScalar, Subsemigroup.op_eq_top, TrivSqZeroExt.invOf_eq_inv, Submonoid.centerToMulOpposite_symm_apply_coe, Subalgebra.unop_sSup, mem_rightCoset, AlgEquiv.toRingEquiv_unop, ValuationSubring.pointwise_central_scalar, normal_iff_eq_cosets, TwoSidedIdeal.mem_asIdealOpposite, TrivSqZeroExt.snd_inv, Subalgebra.unop_le_unop_iff, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyonedaObj, NonUnitalRingHom.toOpposite_apply, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, MulOpposite.instIsOrderedMonoid, MulOpposite.counit_def, TrivSqZeroExt.inl_mul, op_smul_op_smul, Subsemigroup.coe_unop, Submonoid.op_le_iff, Matrix.transposeRingEquiv_apply, MulOpposite.coe_opLinearEquiv_toLinearMap, Submodule.map_op_pow, SeparationQuotient.instIsCentralScalar, MulOpposite.op_natCast, Units.isEmbedding_embedProduct, AddEquiv.mulOp_apply, Subring.op_sInf, Set.op_smul_set_mul_eq_mul_smul_set, isSquare_op_iff, Matrix.vecMul_ofNat, Subring.unop_eq_top, MulOpposite.dist_unop, MulOpposite.opMulEquiv_apply, Subring.unop_sInf, MulAction.stabilizer_subgroup_op, Set.op_smul_inter_nonempty_iff, MeasureTheory.OuterMeasure.instIsCentralScalar, CliffordAlgebra.reverseOpEquiv_opComm, Finset.inv_smul_finset_distribā‚€, MulOpposite.opEquiv_apply, HasFDerivWithinAt.mul_const', instContinuousAddMulOpposite, Polynomial.isCentralScalar, Finset.isCentralScalar, IsScalarTower.op_right, AddMonoid.End.isCentralScalar, Subgroup.Normal.op, Units.coe_unop_opEquiv, CategoryTheory.preservesFiniteColimits_preadditiveCoyonedaObj_of_projective, MulOpposite.nnnorm_op, Sigma.instIsCentralScalar, MulOpposite.toLinearEquiv_opLinearIsometryEquiv, instContinuousNegMulOpposite, MulOpposite.opEquiv_symm_apply, IsLinearTopology.instMulOpposite, ContinuousSMul.op, MulEquiv.inv'_symm_apply, instIsStablyFiniteRingMulOpposite, starMulEquiv_apply, MonoidHom.op_symm_apply_apply, IsTopologicalSemiring.toOppositeIsModuleTopology, Subring.mem_unop, fderiv_pow_ring', MulOpposite.instIsCentralScalar, Subsemigroup.unop_injective, MulEquiv.op_apply_apply, AlgEquiv.toRingEquiv_opOp, Option.instIsCentralScalar, Subsemigroup.op_sup, Subgroup.unop_sInf, Set.inv_smul_set_distribā‚€, MulOpposite.lipschitzMul, HasSum.op, Prod.isIsometricSMul'', rank_dual_eq_card_dual_of_aleph0_le_rank', DoubleCentralizer.instIsCentralScalar, Subring.mem_op, Subalgebra.unop_iInf, CategoryTheory.preservesHomology_preadditiveCoyonedaObj_of_projective, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1, MulOpposite.opLinearEquiv_toAddEquiv, Subsemiring.opEquiv_symm_apply, Subring.unop_le_unop_iff, Subring.centerToMulOpposite_apply_coe, OreLocalization.instIsCentralScalar, Submonoid.op_sup, TrivSqZeroExt.inv_inv, MulOpposite.inner_unop, MulOpposite.op_le_op, MulOpposite.dist_op, AlgEquiv.op_symm_apply_symm_apply, hasSum_op, Subsemigroup.unop_eq_top, Matrix.map_op_smul', MulAction.stabilizer_op_subgroup, TrivSqZeroExt.exp_def, HasFDerivAt.fun_pow', Subalgebra.unop_inf, QuotientGroup.orbit_eq_out_smul, Subsemigroup.centerToMulOpposite_symm_apply_coe, HasMFDerivWithinAt.mul', isUnit_unop, Subsemiring.unop_injective, Module.Finite.instMulOpposite, IsAzumaya.coe_tensorEquivEnd, Subring.unop_inf, CompactlySupportedContinuousMap.instIsCentralScalar, AlgHom.fromOpposite_apply, TrivSqZeroExt.inr_mul_inl, Finset.image_op_mul, Subring.op_eq_bot, Finsupp.isCentralScalar, Subring.op_le_iff, ExteriorAlgebra.toTrivSqZeroExt_ι, TrivSqZeroExt.snd_invOf, QuaternionAlgebra.coe_starAe, isRegular_op, MulOpposite.one_le_unop, LinearMap.toMatrixRight'_id, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, TrivSqZeroExt.inl_mul_inl, instInvariantBasisNumberMulOpposite, Subalgebra.mem_unop, Matrix.conjTransposeRingEquiv_symm_apply, TwoSidedIdeal.op_ringCon, MulOpposite.op_nonpos, MulOpposite.uniformContinuous_op, MulOpposite.unop_le_unop, MulOpposite.unop_zero, MulOpposite.op_list_prod, SMulCommClass.opposite_mid, MulOpposite.op_neg, RingInvo.involution, MulOpposite.unop_nonpos, Subgroup.op_eq_top, Subsemiring.mopRingEquivOp_apply_coe, Subsemiring.op_inf, Subalgebra.op_top, MulOpposite.instIsRightCancelMul, CStarMatrix.instIsCentralScalar, Submonoid.unop_eq_bot, Subgroup.op_sInf, Subalgebra.unop_adjoin, Subsemigroup.op_iSup, Algebra.TensorProduct.opAlgEquiv_symm_apply, hasStrictFDerivAt_pow', Subalgebra.op_iInf, Subgroup.unop_toSubsemigroup, TrivSqZeroExt.isCentralScalar, RingHom.op_symm_apply_apply, IsLeftCancelMulZero.toFaithfulSMul_opposite, Submonoid.unop_le_unop_iff, LieSubmodule.Quotient.isCentralScalar, Polynomial.opRingEquiv_symm_C_mul_X_pow, fderiv_fun_mul', TrivSqZeroExt.liftEquivOfComm_apply, Subring.op_toSubsemiring, Subalgebra.op_le_iff, Derivation.instIsCentralScalar, Set.inv_smul_set_distrib, AlgHom.toRingHom_fromOpposite, Subsemigroup.op_bot, Polynomial.opRingEquiv_symm_monomial, Submodule.linearDisjoint_op, CliffordAlgebra.toBaseChange_comp_reverseOp, AddMonoidHom.instIsCentralScalar, IsOpen.rightCoset, Matrix.vecMulVec_smul', MulOpposite.opLinearIsometryEquiv_symm_apply, SMulCommClass.op_right, AddMonoidHom.mul_op_ext_iff, Submonoid.op_le_op_iff, TrivSqZeroExt.isUnit_inv_iff, Subring.unop_eq_bot, Subring.pointwise_central_scalar, Matrix.kronecker_ofNat, Submonoid.unop_sup, Subsemiring.unop_inf, MulOpposite.instIsOrderedAddMonoid, Matrix.mulVec_eq_sum, Subsemiring.unop_top, Polynomial.support_opRingEquiv, Submonoid.equivOp_apply_coe, rightCoset_mem_rightCoset, MulOpposite.instSubsingleton, TrivSqZeroExt.inv_neg, Submonoid.pointwise_isCentralScalar, Submodule.map_op_mul, Finset.inv_op_smul_finset_distribā‚€, hasStrictFDerivAt_list_prod_attach', MeasureTheory.Lp.instIsCentralScalar, Matrix.scalar_comm_iff, TrivSqZeroExt.sndHom_comp_map, AddMonoidAlgebra.opRingEquiv_single, Subring.unop_bot, RingCon.opOrderIso_symm_apply, isLeftRegular_op, tsum_unop, NonUnitalSeminormedRing.isBoundedSMulOpposite, TrivSqZeroExt.map_comp_map, Subalgebra.algEquivOpMop_apply, Finset.map_op_mul, AlgEquiv.opComm_apply_symm_apply, Subsemigroup.opEquiv_apply, Subsemigroup.op_closure, Set.iUnion_op_smul_set, Subalgebra.op_toSubring, TrivSqZeroExt.snd_mul, Complex.instIsCentralScalarOfReal, Matrix.vecMul_diagonal_const, Unitization.instIsCentralScalar, Submodule.Quotient.isCentralScalar, MulOpposite.op_add, Submodule.isCentralScalar, AddHom.mulOp_symm_apply_apply, RootPairing.Equiv.coweightHom_op, NonUnitalSubring.centerToMulOpposite_symm_apply_coe, Subsemiring.op_sSup, Set.mul_pair, TrivSqZeroExt.algebraMap_eq_inl, RingEquiv.op_symm_apply_symm_apply, AlgHom.toLinearMap_fromOpposite, AlgEquiv.toRingEquiv_op, AddMonoidAlgebra.opRingEquiv_apply, MulOpposite.unop_one, Submonoid.op_inf, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_Ļ€, MulOpposite.commute_op, Con.orderIsoOp_apply, Subgroup.coe_unop, Finset.op_smul_convolution_eq_convolution_smul, Matrix.toLinearMapRight'_apply, Subgroup.equivOp_apply_coe, NonUnitalRingHom.op_apply_apply, Submonoid.unop_sInf, Set.image_op_inv, Subgroup.smul_opposite_mul, HasFDerivWithinAt.pow', Subgroup.opEquiv_symm_apply, measurableSMulā‚‚_opposite_of_mul, MulOpposite.unop_intCast, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, HasFDerivAt.list_prod', hasFDerivAt_pow', Set.mul_subset_iff_right, Subring.ringEquivOpMop_symm_apply_coe, Semigroup.opposite_smulCommClass, Subring.unop_closure, Submonoid.opEquiv_apply, Subsemigroup.op_sInf, MulOpposite.opAddEquiv_toEquiv, Subgroup.unop_eq_top, RingInvo.coe_ringEquiv, DualNumber.commute_eps_left, Matrix.vecMul_natCast, Subgroup.smul_opposite_image_mul_preimage', Subring.unop_toSubsemiring, Subgroup.unop_iSup, Submodule.map_unop_one, TrivSqZeroExt.isUnit_inr_iff, Polynomial.coeff_opRingEquiv, MulOpposite.charP, Module.Basis.mulOpposite_repr_eq, Subring.unop_sup, MulOpposite.instIsOrderedRing, comap_uniformity_mulOpposite, CategoryTheory.Mat.instIsEquivalenceMat_SingleObjMulOppositeEquivalenceSingleObjInverse, Subsemiring.ringEquivOpMop_symm_apply_coe, Submonoid.unop_sSup, AlgEquiv.toAlgHom_unop, AlgEquiv.moduleEndSelf_apply_apply, Quaternion.coe_starAe, MulOpposite.norm_op, isRightRegular_iff, StarSemigroup.toOpposite_starModule, Subring.op_iSup, MulOpposite.unop_mem_center_iff, DomMulAct.stabilizerMulEquiv_apply, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent, MulOpposite.comap_op_leftUniformSpace, AlgHom.toRingHom_unop, Subalgebra.op_iSup, IsSemisimpleRing.instMulOpposite, SubMulAction.isCentralScalar, Algebra.IsCentral.instMulOpposite, MulOpposite.op_one, Subalgebra.op_sup, MulOpposite.unop_list_prod, Submonoid.op_eq_top, IsCentralScalar.isLinearTopology_iff, Subgroup.unop_injective, MulOpposite.instDiscreteTopology, Set.image_op_smul, TrivSqZeroExt.snd_map, Matrix.trace_mul_single, Submonoid.unop_bot, Subsemigroup.unop_sInf, MulOpposite.op_div, isRightRegular_op, AlgEquiv.moduleEndSelfOp_symm_apply, IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite, Subsemigroup.mem_unop, MulOpposite.continuousSMul, Finset.mulETransformRight_fst, UniqueMul.to_mulOpposite, PUnit.instIsCentralScalar, orbit_subgroup_eq_rightCoset, op_geom_sum, DualNumber.commute_eps_right, MulEquiv.opOp_apply, MulOpposite.instStarModule, Units.isClosedEmbedding_embedProduct, UniformContinuousConstSMul.op, MulOpposite.instMeasurableMul, CliffordAlgebra.reverseOp_ι, MulOpposite.map_unop_nhds, Matrix.transposeAlgEquiv_apply, MulOpposite.op_mul, MulOpposite.opHomeomorph_symm_apply, MulOpposite.isStablyFiniteRing_iff, MulOpposite.comap_op_nhds, UniqueProds.instMulOpposite, Matrix.toLinearEquivRight'OfInv_apply, Set.inv_op_smul_set_distrib, MulOpposite.instWeaklyLocallyCompactSpace, Submonoid.op_closure, TrivSqZeroExt.fst_map, isSquare_unop_iff, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, Set.op_smul_set_subset_mul, ContinuousMap.instIsCentralScalar, RingEquiv.op_symm_apply_apply, HasFDerivAt.pow', HasStrictFDerivAt.pow', MulHom.op_apply_apply, AlgHom.toRingHom_op, Subsemigroup.unop_bot, NonUnitalSubsemiring.centerToMulOpposite_apply_coe, Subalgebra.unop_toSubsemiring, Subalgebra.coe_unop, instContinuousInvMulOpposite, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, CentroidHom.instIsCentralScalar, MulOpposite.instNoZeroDivisors, HasStrictFDerivAt.mul_const', instProperSMulSubtypeMulOppositeMemSubgroupOpOfIsTopologicalGroupOfIsClosedCoe, Set.image_op_one, AlgEquiv.opComm_symm_apply_apply, AlgEquiv.moduleEndSelf_symm_apply, Units.coe_opEquiv_symm, MulOpposite.opLinearIsometryEquiv_apply, Units.continuous_embedProduct, Subsemiring.coe_op, Subring.opEquiv_apply, Submodule.comap_unop_pow, Subgroup.op_closure, MulOpposite.instIsLeftCancelMulZeroOfIsRightCancelMulZero, Ideal.pointwise_central_scalar, AlgEquiv.opComm_symm_apply_symm_apply, fderivWithin_list_prod', FreeLieAlgebra.instIsCentralScalar, MulOpposite.rank, SkewMonoidAlgebra.instIsCentralScalar, Subsemiring.op_toSubmonoid, Submonoid.op_injective, HasFDerivWithinAt.fun_mul', ContinuousAlternatingMap.instIsCentralScalar, Submonoid.unop_injective, Subsemiring.unop_bot, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower, Submonoid.mem_op, MulOpposite.instFiniteDimensional, TrivSqZeroExt.algebraMap_eq_inlHom, Subgroup.op_injective, Set.image_op_smul_distrib, Subgroup.op_sup, instProperSMulMulOppositeOfIsTopologicalGroup, Subalgebra.opEquiv_symm_apply, instErgodicSMulMulOppositeOfIsMulRightInvariant, fderivWithin_pow_ring', Subgroup.unop_sSup, Algebra.TensorProduct.opAlgEquiv_tmul, Subgroup.unop_bot, QuotientGroup.orbit_mk_eq_smul, MulOpposite.unop_bijective, Subgroup.op_toSubmonoid, MulOpposite.op_bijective, AlgEquiv.mopMatrix_symm_apply, eq_cosets_of_normal, TwoSidedIdeal.subtypeMop_apply, MulOpposite.coe_opLinearEquiv, Subalgebra.linearEquivOp_symm_apply_coe, CategoryTheory.IsGrothendieckAbelian.instIsLeftAdjointModuleCatMulOppositeEndTensorObj, AlgEquiv.toRingEquiv_toOpposite, HasFDerivWithinAt.fun_pow', Matrix.transposeAlgEquiv_symm_apply, MulOpposite.unop_injective, MulOpposite.unop_surjective, CategoryTheory.Mat.instFullMat_SingleObjMulOppositeEquivalenceSingleObjInverse, MulOpposite.comul_def, Subsemigroup.unop_closure, MulOpposite.isDedekindFiniteMonoid_iff, Polynomial.opRingEquiv_symm_C, Submonoid.mem_unop, MulOpposite.coe_opMulEquiv, Matrix.vecMulVec_mulVec, Subring.op_closure, instIsTopologicalSemiringMulOpposite, Units.embed_product_star, instIsIsometricSMulMulOpposite, TrivSqZeroExt.map_inl, RingCon.instIsCentralScalarQuotient, Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass, IsScalarTower.op_left, HasFDerivAt.mul_const', Subring.opEquiv_symm_apply, summable_op, MulOpposite.unop_inv, HasStrictFDerivAt.fun_pow', MulEquiv.op_symm_apply_symm_apply, Subsemigroup.op_eq_bot, MulOpposite.opLinearEquiv_symm_toAddEquiv, Subsemiring.ringEquivOpMop_apply, AlgEquiv.op_symm_apply_apply, Finset.op_smul_stabilizer_of_no_doubling, MulOpposite.instIsRightCancelAdd, MonoidHom.op_apply_apply, isSemisimpleRing_mulOpposite_iff, Subring.op_inf, MulHom.toOpposite_apply, RingEquiv.unop_map_list_prod, DualNumber.lift_op_smul, Subring.unop_iInf, PowerSeries.substAlgHom_eq_aeval, TrivSqZeroExt.mul_right_eq_one, ContinuousMultilinearMap.instIsCentralScalar, RingHom.fromOpposite_apply, MulOpposite.opContinuousLinearEquiv_apply, Subring.unop_iSup, MulOpposite.op_nonneg, TwoSidedIdeal.coe_unop, Subsemigroup.unop_iInf, isRegular_unop, MulOpposite.op_zpow, AddMonoidHom.mulOp_symm_apply_apply, CategoryTheory.Mat.equivalenceSingleObjInverse_map, UniformSpace.Completion.instIsCentralScalar, Finset.image_op_pow, Matrix.conjTransposeRingEquiv_apply, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimits, Language.reverseIso_symm_apply, MulOpposite.unop_eq_one_iff, SemiconjBy.op, instFaithfulSMulMulOpposite_1, MulOpposite.smul_eq_mul_unop, IsRegular.op, Subgroup.coe_op, Submodule.equivOpposite_symm_apply, Polynomial.natDegree_opRingEquiv, MulOpposite.comap_op_rightUniformSpace, MulOpposite.op_surjective, TwoSidedIdeal.instSMulMemClassMulOpposite, TwoSidedIdeal.coe_op, MonoidAlgebra.isCentralScalar, op_geom_sumā‚‚, MulOpposite.op_intCast, Subsemigroup.le_op_iff, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, MulOpposite.toContinuousLinearEquiv_opLinearIsometryEquiv, Subsemiring.op_top, Submodule.comap_unop_one, MulOpposite.instIsEmpty, starRingEquiv_apply, MulEquiv.op_symm_apply_apply, RingInvo.map_eq_zero_iff, Subsemiring.unop_iInf, MvPolynomial.isCentralScalar, TrivSqZeroExt.inl_mul_eq_smul, Subsemiring.unop_sSup, Con.instIsCentralScalar, Submodule.mulMap_op, Matrix.mulVec_single, hasStrictFDerivAt_list_prod', Subsemiring.unop_eq_bot, TwoSidedIdeal.subtypeMop_injective, MulOpposite.unop_le_one, Subsemigroup.unop_le_unop_iff, TrivSqZeroExt.inv_zero, Ring.uniformContinuousConstSMul_op, Rack.op_act_op_eq, DualNumber.eps_mul_eps, IsUnit.op, ContinuousLinearMap.isCentralScalar, Finset.biUnion_op_smul_finset, Subring.op_eq_top, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, Polynomial.opRingEquiv_op_C_mul_X_pow, IsRightRegular.isSMulRegular, Subsemigroup.coe_op, TrivSqZeroExt.isUnit_inl_iff, MulOpposite.coe_opLinearEquiv_symm_toLinearMap, rightCoset_one, TrivSqZeroExt.isUnit_iff_isUnit_fst, Subsemigroup.op_inf, CategoryTheory.Mat.equivalenceSingleObjInverse_obj_str, MulOpposite.instCompactSpace, Subgroup.op_eq_bot, RingEquiv.opOp_symm_apply, MeasureTheory.Measure.instIsCentralScalar, CategoryTheory.preservesLimits_preadditiveCoyonedaObj, MulHom.fromOpposite_apply, RingHom.op_apply_apply, Matrix.toLinearMapRight'_one, Subsemiring.mopRingEquivOp_symm_apply, HasFDerivWithinAt.mul', Subsemigroup.op_injective, Subgroup.le_op_iff, Subsemigroup.equivOp_apply_coe, Submodule.comap_op_one, Submonoid.unop_closure, RingInvoClass.involution, Subgroup.unop_le_unop_iff, CategoryTheory.additive_coyonedaObj, Commute.op, AlgHom.toOpposite_apply, DualNumber.snd_mul, MulOpposite.instModuleIsReflexive, Subgroup.op.instNormal, leftCoset_rightCoset, TrivSqZeroExt.isUnit_or_isNilpotent, Matrix.conjTranspose_smul_self, Subring.unop_sSup, Subgroup.op_sSup, Submodule.map_op_one, fderivWithin_mul', MulOpposite.unop_comp_op, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, RestrictScalars.isCentralScalar, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, Subalgebra.le_op_iff, Matrix.vecMul_intCast, Subgroup.mem_unop, ULift.instIsCentralScalar, Subgroup.centerToMulOpposite_symm_apply_coe, MulOpposite.continuous_op, Finset.unop_sum, MulOpposite.op_nnratCast, mem_rightCoset_iff, TwoSidedIdeal.mem_unop_iff, MulOpposite.nndist_unop, TrivSqZeroExt.mul_inv_rev, Submonoid.coe_unop, Matrix.scalar_commute_iff, Algebra.TensorProduct.opAlgEquiv_symm_tmul, instFaithfulSMulMulOppositeOfIsLeftCancelMul, tsum_op, Subsemigroup.unop_sSup, Subalgebra.mopAlgEquivOp_apply_coe, MulOpposite.unop_natCast, fderiv_list_prod', Subsemigroup.op_sSup, HasMFDerivAt.mul', Subgroup.unop_sup, NonUnitalSubring.centerToMulOpposite_apply_coe, isLinearTopology_iff_hasBasis_twoSidedIdeal, MulOpposite.instIsDedekindFiniteMonoid, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, Subalgebra.algEquivOpMop_symm_apply_coe, AlgHom.op_symm_apply_apply, MulOpposite.opMulEquiv_symm_apply, Submonoid.op_top, RootPairing.Equiv.coweightHom_toLinearMap, Subgroup.op_le_iff, isRightRegular_unop, Units.range_embedProduct, Subring.ringEquivOpMop_apply, MulOpposite.op_le_one, AlgEquiv.opOp_symm_apply, Set.image_op_mul, RootPairing.Equiv.instSMulCommClassMulOppositeAut, MonoidHom.toOpposite_apply, AddSubgroup.pointwise_isCentralScalar, CliffordAlgebra.reverseOpEquiv_apply, RootPairing.Equiv.coweightHom_apply, HasFDerivAt.fun_mul', LieSubalgebra.instIsCentralScalarSubtypeMem, Subsemigroup.unop_top, Subsemigroup.op_top, MonoidAlgebra.opRingEquiv_apply, Units.embedProduct_injective, IsLeftRegular.op, CategoryTheory.preadditiveCoyoneda_obj, RingEquiv.opOp_apply, AddMonoidAlgebra.isCentralScalar, MulOpposite.opAddEquiv_symm_apply, Subsemiring.unop_toSubmonoid, Finset.map_op_pow, Subsemiring.unop_iSup, MulOpposite.instIsLeftCancelAdd, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, Submonoid.op_bot, MulOpposite.op_comp_unop, MulOpposite.unop_finsuppSum, Submonoid.opEquiv_symm_apply, Units.isInducing_embedProduct, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, Subsemiring.mem_unop, HasFDerivAt.mul', Subgroup.normal_unop, rightCoset_assoc, Finset.op_sum, hasFDerivAt_list_prod_attach', Subgroup.smul_diff', QuotientGroup.sound, MulOpposite.rankCondition_iff, Subgroup.unop_toSubmonoid, Subalgebra.op_le_op_iff, Matrix.op_smul_eq_vecMul, MulOpposite.unop_div, Finset.mulETransformLeft_fst, MulOpposite.op_inv, TrivSqZeroExt.mul_inl_eq_op_smul, MulOpposite.semiconjBy_unop, IsCentralScalar.op_smul_eq_smul, Matrix.kronecker_diagonal, Subsemigroup.unop_inf, Finset.mul_singleton, op_smul_mul, instContinuousStarMulOpposite, QuadraticAlgebra.instIsCentralScalar, MulOpposite.isCancelAdd_iff, isLeftRegular_unop, Subgroup.unop_iInf, Polynomial.opRingEquiv_symm_X, Subsemiring.coe_unop, LinearMap.toMatrixRight'_comp, ContinuousAffineMap.instIsCentralScalar, Subsemiring.op_iInf, TrivSqZeroExt.inv_inr, IsLinearTopology.hasBasis_right_ideal, Submodule.comap_unop_mul, Finset.smul_inv_mul_opSMul_eq_mul_of_doubling_lt_three_halves, TensorProduct.instIsCentralScalar, Module.Basis.repr_unop_eq_mulOpposite_repr, NormedSpace.exp_unop, CategoryTheory.IsGrothendieckAbelian.instIsRightAdjointModuleCatMulOppositeEndPreadditiveCoyonedaObj, DualNumber.isNilpotent_eps, MulOpposite.uniformContinuous_unop, Subalgebra.opEquiv_apply, AlternatingMap.instIsCentralScalar, TrivSqZeroExt.eq_smul_exp_of_invertible, MulOpposite.unop_nonneg, Set.inv_op_smul_set_distribā‚€, measurable_mul_unop, Subring.addEquivOp_symm_apply_coe, RingInvoClass.toRingEquivClass, TrivSqZeroExt.map_id, ContinuousMul.to_continuousSMul_op, ContinuousConstSMul.op, Subsemigroup.op_le_iff, Submonoid.unop_toSubsemigroup, AlgHom.mulLeftRightMatrix.comp_inv, Units.embedProduct_apply, MulOpposite.op_sub, MulOpposite.semiconjBy_op, Subgroup.isQuotientCoveringMap, Submonoid.op_toSubsemigroup, MulOpposite.opHomeomorph_apply, RingEquiv.moduleEndSelfOp_symm_apply, Submodule.pointwiseCentralScalar, MulOpposite.instIsLeftCancelMul, FormalMultilinearSeries.ofScalarsSum_unop, TwoSidedIdeal.unop_ringCon, MulOpposite.instT2Space, instFaithfulSMulMulOpposite, Subgroup.opEquiv_apply, MulOpposite.isLeftCancelMulZero_iff, DoubleCentralizer.toProdMulOppositeHom_apply, IsAzumaya.AlgHom.mulLeftRight_bij, IsClosed.rightCoset, Rack.op_invAct_op_eq, MulOpposite.unop_eq_zero_iff, HasFDerivWithinAt.list_prod', Subalgebra.unop_iSup, uniformity_mulOpposite, Subalgebra.unop_sInf, TwoSidedIdeal.coe_mop_smul, Matrix.col_vecMulVec, Finset.convolution_op_smul_eq_convolution_mul_inv, Subsemiring.op_bot, fderivWithin_pow', Summable.op, MonoidHom.fromOpposite_apply, MulOpposite.unop_smul_eq_unop_smul_unop, Subgroup.unop_top, MulOpposite.instSMulCommClass

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