Documentation Verification Report

Basic

📁 Source: Mathlib/Algebra/Notation/Pi/Basic.lean

Statistics

MetricCount
DefinitionsmulSingle, single
2
Theoremsapply_mulSingle, apply_mulSingle₂, apply_single, apply_single₂, curry_mulSingle, curry_single, mulSingle_apply, mulSingle_comm, mulSingle_eq_of_ne, mulSingle_eq_of_ne', mulSingle_eq_one_iff, mulSingle_eq_same, mulSingle_inj, mulSingle_injective, mulSingle_ne_one_iff, mulSingle_one, mulSingle_op, mulSingle_op₂, single_apply, single_comm, single_eq_of_ne, single_eq_of_ne', single_eq_same, single_eq_zero_iff, single_inj, single_injective, single_ne_zero_iff, single_op, single_op₂, single_zero, uncurry_mulSingle_mulSingle, uncurry_single_single
32
Total34

Pi

Definitions

NameCategoryTheorems
mulSingle 📖CompOp
88 mathmath: update_eq_div_mul_mulSingle, Subgroup.mulSingle_mem_pi, Finset.univ_prod_mulSingle, mulSupport_mulSingle_subset, curry_mulSingle, mulSingle_mul_mulSingle_eq_mulSingle_mul_mulSingle, apply_mulSingle₂, Set.image_mulSingle_Ioo, Fin.insertNth_one_right, star_mulSingle, mulSingle_div, Set.image_mulSingle_Icc_right, mulSingle_eq_same, Set.image_mulSingle_uIcc_left, Set.mulIndicator_singleton, Set.image_mulSingle_Ioo_right, mulSingle_op₂, mulSingle_mul, mulSupport_mulSingle_one, subsingleton_mulSupport_mulSingle, Finset.prod_pi_mulSingle, mulSingle_one, mulSingle_pow, Finset.prod_pi_mulSingle', mulSingle_comp_equiv, mulSingle_multiplicativeOfAdd_eq, mulSupport_mulSingle, Set.image_mulSingle_uIcc, MonoidHom.noncommPiCoprod_mulSingle, single_additiveOfMul_eq, mulSingle_comm, Set.image_mulSingle_Ioo_left, mulSingle_inv, Set.image_mulSingle_Icc, mulSingle_zpow, Fintype.prod_pi_mulSingle', Set.image_mulSingle_Icc_left, Fintype.prod_pi_mulSingle, FreeMonoid.count_of, Finset.noncommProd_mulSingle, one_le_mulSingle, MonoidHom.mulSingle_apply, Subgroup.noncommPiCoprod_mulSingle, hasProd_pi_single, mulSingle_eq_one_iff, Set.image_mulSingle_uIcc_right, Sigma.uncurry_mulSingle_mulSingle, Sum.elim_mulSingle_one, mulSingle_le_one, OneHom.coe_mulSingle, MonoidHom.coe_mulSingle, mulSingle_sup, OneHom.mulSingle_apply, orderOf_piMulSingle, mulSingle_apply, Set.image_mulSingle_Ico_left, Fin.insertNth_div_same, RestrictedProduct.comp_mulSingle, RestrictedProduct.coe_mulSingle_apply, mulSingle_op, mulSingle_strictMono, Set.image_mulSingle_Ioc_right, Finset.noncommProd_mul_single, mulSingle_apply_commute, Submonoid.mulSingle_mem_pi, mulSingle_eq_of_ne, mulSingle_inf, mulSingle_eq_of_ne', Sum.elim_one_mulSingle, Monoid.CoprodI.of_leftInverse, mulSingle_injective, Set.image_mulSingle_Ico_right, mulSingle_inj, continuous_mulSingle, NNReal.coe_mulSingle, uncurry_mulSingle_mulSingle, Subsingleton.pi_mulSingle_eq, apply_mulSingle, Set.image_mulSingle_Ioc, Set.image_mulSingle_Ico, Sigma.curry_mulSingle, PiTensorProduct.algebraMap_apply, mulSupport_mulSingle_disjoint, tprod_pi_single, mulSingle_mono, Set.image_mulSingle_Ioc_left, mulSingle_le_mulSingle, mulSupport_mulSingle_of_ne
single 📖CompOp
280 mathmath: single_mono, Matrix.single_eq_updateRow_zero, subsingleton_support_single, RingHom.ker_evalRingHom, Matrix.single_vecMul, Ideal.single_mem_pi, Matrix.cramer_transpose_row_self, hasSum_pi_single, Set.image_single_uIcc_right, Isometry.single, FreeAddMonoid.count_of, Finsupp.weight_single_one_apply, QuadraticMap.Isometry.proj_comp_single_of_same, nnnorm_single, stdSimplex_fin_two, Matrix.cramer_row_self, linearIndependent_single, LinearMap.BilinForm.toMatrix'_apply, QuadraticMap.Isometry.single_apply, DFinsupp.equivFunOnFintype_single, AddSubgroup.noncommPiCoprod_single, Matrix.mulVec_single_one, single_apply_smul, single_comp_equiv, Finset.univ_sum_single, single_nonpos, PiLp.norm_toLp_single, ContinuousLinearMap.single_apply, HahnSeries.single.addMonoidHom_apply_coeff, star_single, stdSimplexHomeomorphUnitInterval_zero, Subsingleton.pi_single_eq, Matrix.diagonal_updateRow_single, Fintype.bilinearCombination_apply_single, BoxIntegral.hasIntegral_GP_pderiv, support_single, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, single_mul_left_apply, Sum.elim_single_zero, FormalMultilinearSeries.ofScalars_apply_zero, Matrix.toLinearMapₛₗ₂'_single, AddSubmonoid.single_mem_pi, segment_single_subset_stdSimplex, linearIndependent_single_of_ne_zero, Matrix.single_eq_single_vecMulVec_single, single_star, uncurry_single_single, basis_repr_single, Matrix.IsHermitian.eigenvectorUnitary_mulVec, single_zero, Matrix.toLinearMap₂'Aux_single, single_apply, single_op₂, support_single_of_ne, lp.coeFn_single, Matrix.one_eq_pi_single, single_mem_stdSimplex, AddSubgroup.single_mem_pi, single_add, single_inf, Set.image_single_Icc_left, Ideal.span_single_eq_top, basis_apply, PiLp.nndist_toLp_single_same, LinearMap.toBilin'Aux_toMatrixAux, Set.image_single_Ioc, PiLp.nnnorm_toLp_single, Finset.noncommSum_single, apply_single, toBilin'Aux_toMatrixAux, Matrix.row_diagonal, single_mul_right, Fintype.sum_single_smul, HahnSeries.SummableFamily.single_toFun, orthonormalBasis_apply, mulSingle_multiplicativeOfAdd_eq, single_inj, MvPolynomial.pderiv_X, Finsupp.linearCombination_single_index, hasDerivAt_update, nndist_single_single, single_additiveOfMul_eq, Matrix.circulant_single_one, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, single_dotProduct, AddMonoidHom.single_apply, single_sub, Matrix.vec_single, single_eq_of_ne, RestrictedProduct.coe_single_apply, pi_eq_sum_univ', Finsupp.linearEquivFunOnFinite_single, ordinaryHypergeometricSeries_apply_zero, LinearMap.toMatrixAlgEquiv'_apply, RestrictedProduct.comp_single, PiToModule.fromMatrix_apply_single_one, MvPolynomial.pderiv_def, RingHom.functions_ext_iff, stdSimplex.vertex_coe, Matrix.diagonal_updateCol_single, enorm_single, single_sup, PiLp.basisFun_apply, LinearIsometryEquiv.piLpCongrRight_single, DirectSum.linearEquivFunOnFintype_lof, single_one_dotProduct, Matrix.adjugate_apply, LinearMap.toMatrix'_apply, single_smul, TensorProduct.piRight_symm_single, CStarMatrix.toCLM_apply_single, Set.image_single_Ioo_left, support_single_subset, CompleteOrthogonalIdempotents.single, Set.image_single_Ioo_right, QuadraticMap.Isometry.proj_comp_single_of_ne, dist_single_single, Matrix.mul_adjugate_apply, Finsupp.weight_single_index, Matrix.toBilin'Aux_single, Sigma.curry_single, NormedSpace.expSeries_apply_zero, EuclideanSpace.toLp_single, deriv_update, Matrix.projVandermonde_apply_zero_right, LinearMap.pi_ext_iff, DFinsupp.sumAddHom_piSingle, Matrix.rectVandermonde_apply_zero_right, hasFDerivAt_single, QuadraticMap.pi_apply_single, Algebra.PreSubmersivePresentation.aevalDifferential_single, WithCStarModule.norm_single, norm_single, fderiv_update, CStarMatrix.mul_entry_mul_eq_inner_toCLM, PiToModule.fromEnd_apply_single_one, Set.image_single_Ioo, single_smul₀, TensorProduct.single_tmul, LinearMap.apply_single, WithCStarModule.inner_single_right, support_single_disjoint, dotProduct_single_one, MultilinearMap.dfinsuppFamily_single_left_apply, Matrix.adjugate_def, dotProduct_single, Set.image_single_Icc_right, Matrix.diagonal_mulVec_single, PiLp.dist_toLp_single_same, QuadraticMap.Isometry.proj_apply, single_comm, endVecAlgEquivMatrixEnd_apply_apply, MultilinearMap.piFamily_single_left_apply, deriv_single, single_apply_addCommute, TensorProduct.piScalarRight_symm_single, hasFDerivAt_update, Fintype.sum_pi_single, FunOnFinite.map_piSingle, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Finset.noncommSum_add_single, EuclideanSpace.ofLp_single, DFinsupp.sumZeroHom_piSingle, MultilinearMap.piFamily_single_left, LinearMap.coe_single, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, LinearMap.sum_single_apply, TensorProduct.tmul_single, ZeroHom.single_apply, Matrix.Module.single_smul, Set.image_single_Ico_left, single_add_single_eq_single_add_single, Matrix.toLinearMap₂'_single, stdSimplexHomeomorphUnitInterval_one, Matrix.col_diagonal, Sigma.uncurry_single_single, IsAdjoinRootMonic.coeff_algebraMap, Matrix.diag_single_same, Finset.sum_pi_single', Sum.elim_zero_single, contDiff_single, Set.image_single_uIcc_left, single_injective, Finsupp.linearEquivFunOnFinite_symm_single, Finset.sum_pi_single, basisFun_apply, mapsTo_tangentConeAt_pi, continuous_single, Submodule.piQuotientLift_single, single_nonneg, single_op, PiLp.edist_toLp_single_same, single_zsmul, Matrix.of_symm_single, Matrix.single_eq_of_single_single, Matrix.circulant_single, IsAdjoinRootMonic.coeff_one, Set.image_single_Ico, finPiFinEquiv_single, Set.image_single_uIcc, single_smul', WithCStarModule.inner_single_left, AddMonoidHom.coe_single, single_nsmul, curry_single, Set.image_single_Icc, stdSimplex.barycenter_eq_centerMass, tsum_pi_single, LinearMap.single_apply, FunOnFinite.linearMap_piSingle, linearIndependent_single_one, single_mul_left, comul_single, LinearIsometryEquiv.piLpCongrLeft_single, Matrix.single_eq_updateCol_zero, update_eq_sub_add_single, MultilinearMap.piFamily_single, hasDerivAt_single, Set.image_single_Ioc_left, single_eq_zero_iff, lp.single_apply, single_neg, Fin.insertNth_zero_right, UnitAddTorus.mFourier_single, MulHom.single_apply, ZeroHom.coe_single, PEquiv.transpose_toMatrix_toPEquiv_apply, DirectSum.linearEquivFunOnFintype_symm_single, Fintype.linearCombination_apply_single, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, Finsupp.equivFunOnFinite_symm_single, convexHull_rangle_single_eq_stdSimplex, Basis.equivFun_symm_single, single_eq_of_ne', Matrix.diagonal_single, Matrix.single_one_vecMul, Matrix.mulVec_single, IsAdjoinRootMonic.coeff_root, Finsupp.single_eq_pi_single, single_eq_same, Set.image_single_Ico_right, AddMonoidHom.noncommPiCoprod_single, single_strictMono, Set.image_single_Ioc_right, Finsupp.equivFunOnFinite_single, LinearMap.toMatrixₛₗ₂'_apply, Module.Basis.coe_ofEquivFun, support_single_zero, MultilinearMap.dfinsuppFamily_single_left, LinearMap.lsum_piSingle, DFinsupp.single_eq_pi_single, PEquiv.toMatrix_toPEquiv_apply, mem_span_range_single_inl_iff, SkewMonoidAlgebra.coeff_single, Set.indicator_singleton, apply_single₂, stdSimplexEquivIcc_one, finFunctionFinEquiv_single, LinearMap.toMatrix₂'_apply, single_le_single, fderiv_single, BumpCovering.coe_single, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, Matrix.single_vecMul_diagonal, DFinsupp.equivFunOnFintype_symm_single, single_mul_right_apply, counit_single, NNReal.coe_single, IsAdjoinRootMonic.coeff_root_pow, Fin.insertNth_sub_same, parallelepiped_single, CStarMatrix.toCLM_apply_single_apply, LinearMap.toLinearMap₂'Aux_toMatrix₂Aux, Matrix.gram_single, Matrix.toBilin'_single, single_mul, stdSimplexEquivIcc_zero, Fintype.sum_pi_single', LinearEquiv.piRing_apply, fourierCoeff_fourier

Theorems

NameKindAssumesProvesValidatesDepends On
apply_mulSingle 📖mathematicalmulSingleFunction.update.congr_simp
Function.apply_update
apply_mulSingle₂ 📖mathematicalmulSinglemulSingle_eq_same
mulSingle_eq_of_ne
apply_single 📖mathematicalsingleFunction.update.congr_simp
Function.apply_update
apply_single₂ 📖mathematicalsinglesingle_eq_same
single_eq_of_ne
curry_mulSingle 📖mathematicalmulSingle
instOne
Function.curry_update
curry_single 📖mathematicalsingle
instZero
Function.curry_update
mulSingle_apply 📖mathematicalmulSingleFunction.update_apply
mulSingle_comm 📖mathematicalmulSinglemulSingle_apply
mulSingle_eq_of_ne 📖mathematicalmulSingleFunction.update_of_ne
mulSingle_eq_of_ne' 📖mathematicalmulSinglemulSingle_eq_of_ne
mulSingle_eq_one_iff 📖mathematicalmulSingle
instOne
mulSingle_eq_same
one_apply
mulSingle_one
mulSingle_eq_same 📖mathematicalmulSingleFunction.update_self
mulSingle_inj 📖mathematicalmulSinglemulSingle_injective
mulSingle_injective 📖mathematicalmulSingleFunction.update_injective
mulSingle_ne_one_iff 📖Iff.ne
mulSingle_eq_one_iff
mulSingle_one 📖mathematicalmulSingle
instOne
Function.update_eq_self
mulSingle_op 📖mathematicalmulSingleapply_mulSingle
mulSingle_op₂ 📖mathematicalmulSingleapply_mulSingle₂
single_apply 📖mathematicalsingleFunction.update_apply
single_comm 📖mathematicalsinglesingle_apply
single_eq_of_ne 📖mathematicalsingleFunction.update_of_ne
single_eq_of_ne' 📖mathematicalsinglesingle_eq_of_ne
single_eq_same 📖mathematicalsingleFunction.update_self
single_eq_zero_iff 📖mathematicalsingle
instZero
single_eq_same
zero_apply
single_zero
single_inj 📖mathematicalsinglesingle_injective
single_injective 📖mathematicalsingleFunction.update_injective
single_ne_zero_iff 📖Iff.ne
single_eq_zero_iff
single_op 📖mathematicalsingleapply_single
single_op₂ 📖mathematicalsingleapply_single₂
single_zero 📖mathematicalsingle
instZero
Function.update_eq_self
uncurry_mulSingle_mulSingle 📖mathematicalmulSingle
instOne
Function.uncurry_update_update
uncurry_single_single 📖mathematicalsingle
instZero
Function.uncurry_update_update

---

← Back to Index