Documentation Verification Report

Fold

πŸ“ Source: Mathlib/Data/Finset/Lattice/Fold.lean

Statistics

MetricCount
Definitionsinf, inf', sup, sup'
4
Theoremsinf_eq_bot_iff, sup_eq_top_iff, codisjoint_inf_left, codisjoint_inf_right, coe_inf', coe_inf_of_nonempty, coe_sup', coe_sup_of_nonempty, comp_inf'_eq_inf'_comp, comp_inf_eq_inf_comp, comp_inf_eq_inf_comp_of_is_total, comp_sup'_eq_sup'_comp, comp_sup_eq_sup_comp, comp_sup_eq_sup_comp_of_is_total, comp_sup_eq_sup_comp_of_nonempty, compl_inf, compl_sup, disjoint_sup_left, disjoint_sup_right, exists_inf_eq_iInf, exists_inf_le, exists_mem_eq_inf, exists_mem_eq_inf', exists_mem_eq_sup, exists_mem_eq_sup', exists_sup_eq_iSup, exists_sup_ge, inf'_apply, inf'_comm, inf'_comp_eq_image, inf'_comp_eq_map, inf'_congr, inf'_cons, inf'_const, inf'_eq_inf, inf'_eq_of_forall, inf'_image, inf'_induction, inf'_insert, inf'_le, inf'_le_iff, inf'_le_of_le, inf'_lt_iff, inf'_map, inf'_mem, inf'_mono, inf'_singleton, inf'_sup_distrib_left, inf'_sup_distrib_right, inf'_union, inf_apply, inf_attach, inf_coe, inf_comm, inf_congr, inf_cons, inf_const, inf_def, inf_disjSum, inf_dite_neg_le, inf_dite_pos_le, inf_empty, inf_eq_bot_iff, inf_eq_iInf, inf_eq_sInf_image, inf_eq_top_iff, inf_erase_top, inf_himp_right, inf_id_eq_sInf, inf_id_set_eq_sInter, inf_image, inf_induction, inf_inf, inf_insert, inf_ite, inf_le, inf_le_iff, inf_le_of_le, inf_lt_iff, inf_map, inf_mem, inf_mono, inf_mono_fun, inf_of_mem, inf_sdiff_left, inf_sdiff_right, inf_set_eq_iInter, inf_singleton, inf_sup_distrib_left, inf_sup_distrib_right, inf_top, inf_union, isGLB_inf, isGLB_inf', isGLB_inf_id, isLUB_sup, isLUB_sup', isLUB_sup_id, le_inf, le_inf', le_inf'_iff, le_inf_const_le, le_inf_iff, le_sup, le_sup', le_sup'_iff, le_sup'_of_le, le_sup_dite_neg, le_sup_dite_pos, le_sup_iff, le_sup_of_le, lt_inf'_iff, lt_inf_iff, lt_sup'_iff, lt_sup_iff, mem_inf', mem_sup, mem_sup', ofDual_inf, ofDual_inf', ofDual_sup, ofDual_sup', subset_range_sup_succ, sup'_apply, sup'_comm, sup'_comp_eq_image, sup'_comp_eq_map, sup'_congr, sup'_cons, sup'_const, sup'_eq_of_forall, sup'_eq_sup, sup'_image, sup'_induction, sup'_inf_distrib_left, sup'_inf_distrib_right, sup'_insert, sup'_le, sup'_le_iff, sup'_lt_iff, sup'_map, sup'_mem, sup'_mono, sup'_mono_fun, sup'_singleton, sup'_union, sup_apply, sup_attach, sup_bot, sup_coe, sup_comm, sup_congr, sup_cons, sup_const, sup_const_le, sup_def, sup_disjSum, sup_empty, sup_eq_bot_iff, sup_eq_bot_of_isEmpty, sup_eq_iSup, sup_eq_sSup_image, sup_eq_top_iff, sup_erase_bot, sup_himp_left, sup_himp_right, sup_id_eq_sSup, sup_id_set_eq_sUnion, sup_image, sup_induction, sup_inf_distrib_left, sup_inf_distrib_right, sup_insert, sup_ite, sup_le, sup_le_iff, sup_le_of_le_directed, sup_lt_iff, sup_map, sup_mem, sup_mem_of_nonempty, sup_mono, sup_mono_fun, sup_of_mem, sup_sdiff_left, sup_sdiff_right, sup_set_eq_biUnion, sup_singleton, sup_singleton_apply, sup_singleton_eq_self, sup_sup, sup_toFinset, sup_union, toDual_inf, toDual_inf', toDual_sup, toDual_sup', foldr_inf_eq_inf_toFinset, foldr_sup_eq_sup_toFinset, count_finset_sup, map_finset_sup, mem_sup, map_finset_inf, map_finset_inf', map_finset_sup, map_finset_sup'
206
Total210

Finset

Definitions

NameCategoryTheorems
inf πŸ“–CompOp
168 mathmath: coe_inf', inf_sigma, Set.Finite.einfsep, exists_mem_eq_inf, Set.einfsep_of_fintype, AlgebraicTopology.NormalizedMooreComplex.obj_d, inf_id_set_eq_sInter, le_inf_div, InfPrime.finset_inf_le, min_eq_inf_withTop, inf_eq_top_iff, ContinuousWithinAt.finset_inf_apply, inf_lt_iff, ContinuousAt.finset_inf, List.foldr_inf_eq_inf_toFinset, compl_inf, inf_ite, inf_inf, ofDual_inf, inf_map, inf_le_iff, inf_sub_left, Ideal.comap_finsetInf, Submodule.colon_finsetInf, inf_biUnion, inf_sup_distrib_right, compl_sup, inclusion_exclusion_card_inf_compl, isBoundedUnder_ge_finset_inf, inf_id_eq_sInf, inf_mul_left, OrderIso.infIrredUpperSet_symm_apply, ContinuousOn.finset_inf_apply, Ideal.isPrimary_finsetInf, inf_zero, inf_prodMap, Set.Finset.coe_einfsep, Ideal.prod_le_inf, Submodule.mem_finset_inf, le_inf_imageβ‚‚, le_inf_add, inf_union, ContinuousOn.finset_inf, inf_sup, inf_mem, inf_sup_distrib_left, inf_apply, Ideal.IsPrime.inf_le', ContinuousAt.finset_inf_apply, inf_himp_right, inf_congr, isGLB_inf, inf_induction, inf_const, inf_eq_of_min, Ideal.isPrimary_finset_inf, AddMonoidAlgebra.le_inf_support_add, inf_image, inf_sub_right, PrimitiveSpectrum.hull_finsetInf, inclusion_exclusion_sum_inf_compl, inf_mono_fun, Submodule.IsMinimalPrimaryDecomposition.inf_eq, AddMonoidAlgebra.le_inf_support_pow, mul_inf_le_inf_mul_of_nonneg, inf_product_left, inf_def, inf_inv, inf_attach, Seminorm.closedBall_finset_sup, Topology.IsLocallyConstructible.finsetInf, Submodule.comap_finsetInf, Submodule.coe_finsetInf, ContinuousWithinAt.finset_inf, inf_product_right, TopologicalSpace.Closeds.coe_finset_inf, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_isLimit_lift, inf_eq_bot_iff, AddMonoidAlgebra.le_inf_support_list_prod, le_inf_mul, inf_imageβ‚‚_left, inf_comm, inf_sdiff_right, TopologicalSpace.Opens.coe_finset_inf, inf_dite_neg_le, inf_insert, comp_inf_eq_inf_comp_of_is_total, inf_set_eq_iInter, Ideal.finset_inf_span_singleton, InfClosed.finsetInf_mem, inf_add_left, map_finset_inf, toDual_inf, CategoryTheory.Limits.CompleteLattice.finite_limit_eq_finset_univ_inf, sup_inf, lt_inf_iff, le_inf_iff, PrimitiveSpectrum.preimage_upperClosure_compl_finset, inf_mono, inf_add_right, Nonempty.inf_eq_bot_iff, Submodule.IsMinimalPrimaryDecomposition.minimal, inf_dite_pos_le, IsDedekindDomain.inf_prime_pow_eq_prod, coe_inf_of_nonempty, CategoryTheory.Subobject.finset_inf_factors, Continuous.finset_inf_apply, inf_of_mem, inf_eq_of_isMinOn, inf_mul_right, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_pt, trop_inf, AddMonoidAlgebra.le_inf_support_mul, exists_infIrred_decomposition, inf_empty, mem_inf, exists_inf_le, toDual_sup, untrop_sum', comp_inf_eq_inf_comp, inf_coe, inf_le_of_le, sup_sdiff_left, inf_erase_top, AlgebraicTopology.NormalizedMooreComplex.objX_add_one, inf_sup_inf, Continuous.finset_inf, inf_eq_sInf_image, sup_himp_right, inf_eq_iInf, inf_imageβ‚‚_right, inf_singleton, isGLB_inf_id, Ideal.eq_inf_of_isPrime_inf, Submodule.finset_inf_coe, Submodule.mem_finsetInf, liminf_finset_inf, le_inf, inf_sdiff_left, exists_inf_eq_iInf, inf_le, Filter.Tendsto.finset_inf_nhds_apply, inf_div_left, inf_univ_eq_iInf, inf_disjSum, Set.definable_finset_inf, inf_div_right, inf_neg, inf'_eq_inf, inf_top, inf_one, le_inf_const_le, AddMonoidAlgebra.le_inf_support_finset_prod, Seminorm.ball_finset_sup, AddMonoidAlgebra.le_inf_support_multiset_prod, Ideal.radical_finset_inf, codisjoint_inf_left, CategoryTheory.Subobject.finset_inf_arrow_factors, le_inf_sub, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_Ο€_app, Filter.Tendsto.finset_inf_nhds, inf_Ici, IsRetrocompact.finsetInf, inf_cons, ofDual_sup, Submodule.isPrimary_finsetInf, CategoryTheory.Limits.CompleteLattice.finite_product_eq_finset_inf, codisjoint_inf_right
inf' πŸ“–CompOp
92 mathmath: inf'_inv, coe_inf', Continuous.finset_inf', ContinuousOn.finset_inf'_apply, inf'_univ_eq_ciInf, inf'_sup_inf', inf'_zero, inf'_comm, inf'_lt_iff, ContinuousMap.coe_inf', le_inf'_iff, inf'_product_left, inf'_mem, inf'_congr, inf'_map, Set.Finite.infsep_of_nontrivial, coe_infsep_of_offDiag_nonempty, Set.Nontrivial.infsep_of_fintype, Set.Finite.infsep, inf'_const, inf'_sup_distrib_right, inf'_one, IsRetrocompact.finsetInf', ContinuousOn.finset_inf', inf'_pow, inf'_Ici, inf'_prodMap, le_inf'_imageβ‚‚, toDual_inf', ofDual_sup', Set.infsep_of_fintype, map_finset_inf', inf'_imageβ‚‚_right, Filter.Tendsto.finset_inf'_nhds_apply, nsmul_inf', coe_infsep, inclusion_exclusion_card_biUnion, inf'_product_right, ContinuousMap.inf'_apply, ContinuousWithinAt.finset_inf'_apply, isCoboundedUnder_ge_finset_inf', inf'_comp_eq_image, CompactlySupportedContinuousMap.finsetInf'_apply, inf'_cons, ContinuousAt.finset_inf', comp_inf'_eq_inf'_comp, prodMk_inf'_inf', Nat.cast_finsetInf', ContinuousAt.finset_inf'_apply, lt_inf'_iff, ContinuousWithinAt.finset_inf', inclusion_exclusion_sum_biUnion, liminf_finset_inf', inf'_biUnion, inf'_image, inf_le_centerMass, le_inf', mem_inf', Filter.Tendsto.finset_inf'_nhds, inf'_le_iff, inf'_comp_eq_map, CompactlySupportedContinuousMap.coe_finsetInf', Continuous.finset_inf'_apply, inf'_imageβ‚‚_left, ofDual_inf', inf'_induction, Seminorm.closedBall_finset_sup', inf'_mono, inf'_id_eq_csInf, inf'_neg, inf'_singleton, inf'_eq_csInf_image, InfClosed.finsetInf'_mem, isBoundedUnder_ge_finset_inf', inf'_sup_distrib_left, inf'_eq_inf, inf'_le_of_le, Topology.IsLocallyConstructible.finsetInf', finsetInf'_mem_infClosure, isGLB_inf', ConvexOn.inf_le_of_mem_convexHull, inf'_eq_of_forall, inf'_apply, inf'_mul_le_mul_inf'_of_nonneg, Seminorm.ball_finset_sup', inf'_insert, inf'_union, min'_eq_inf', exists_mem_eq_inf', inf'_le, toDual_sup', truncatedInf_of_mem
sup πŸ“–CompOp
284 mathmath: SchwartzMap.norm_toLp_le_seminorm, AddMonoidAlgebra.sup_support_list_prod_le, sup_one, Seminorm.isBounded_const, sup_add_sup, sup_singleton_eq_self, comp_sup_eq_sup_comp_of_is_total, Seminorm.le_finset_sup_apply, sup_product_right, Finpartition.combine_parts, ContinuousAt.finset_sup, bind_def, Seminorm.finset_sup_apply, WithSeminorms.mem_nhds_iff, CompleteLattice.isCompactElement_finsetSup, Ideal.sum_eq_sup, sup_le_of_le_directed, Pi.norm_def', sup_add_le, comp_sup_eq_sup_comp, Continuous.finset_sup, sup_insert, Nonempty.sup_eq_top_iff, compl_inf, CategoryTheory.Limits.CompleteLattice.finite_coproduct_eq_finset_sup, mem_sup, isWF_sup, ofDual_inf, sup_coe, MvPolynomial.degreeOf_sum_le, compl_sup, sup_induction, MvPolynomial.totalDegree_eq, sup_div_right, sup_erase_bot, WithSeminorms.tendsto_nhds', sup_singleton, MvPolynomial.degrees_def, TopologicalSpace.NoetherianSpace.exists_finset_irreducible, support_sum_subset, sup_set_eq_biUnion, sup_div_le, sup_univ_eq_ciSup, Multiset.sup_powerset_len, SeminormFamily.finset_sup_comp, CategoryTheory.Subobject.finset_sup_factors, sup_Ioc_disjointed_of_monotone, Submodule.finiteDimensional_finset_sup, seq_def, Fintype.sup_disjointed, inf_sup, OrderIso.supIrredLowerSet_symm_apply, isLUB_sup_id, exists_supIrred_decomposition, Set.definable_finset_sup, le_sup_dite_pos, Subgroup.FG.finset_sup, Multiset.finset_sum_eq_sup_iff_disjoint, inf_himp_right, sup_inf_distrib_left, sup_mul_le, max_eq_sup_coe, Filter.Tendsto.finset_sup_nhds, sup_product_left, AddMonoidAlgebra.sup_support_multiset_prod_le, partialSups_eq_sup_range, Polynomial.natDegree_sum_eq_of_disjoint, CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSup, Seminorm.finset_sup_apply_lt, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_ΞΉ_app, MeasureTheory.preVariation.Finset.sup_measurableSetSubtype_eq_biUnion, subset_range_sup_succ, Submonoid.FG.finset_sup, BoxIntegral.Prepartition.distortion_biUnionTagged, sup_Iic, coe_sup', Seminorm.bound_of_continuous, SupIndep.disjoint_sup_sup, disjoint_sup_left, sup_empty, sup_sub_right, sup_attach, MonomialOrder.degree_sum_le, ContinuousOn.finset_sup_apply, sup_const, Seminorm.closedBall_finset_sup, TopologicalSpace.Opens.coe_finset_sup, CategoryTheory.Limits.CompleteLattice.finite_colimit_eq_finset_univ_sup, Polynomial.degree_sum_le, mem_sup_support_iff, sup_eq_top_iff, sup_const_le, nilpotencyClass_pi, sup_inf_distrib_right, WithSeminorms.isOpen_iff_mem_balls, coe_sup_of_nonempty, sup_prodMap, exists_sup_ge, NNReal.mul_finset_sup, sup_sub_le, sup_lt_iff, Pi.nnnorm_def', max_eq_sup_withBot, sup_le, Submodule.fg_finset_sup, sup_zero, TopologicalSpace.Clopens.exists_finset_eq_sup_prod, SimpleGraph.extremalNumber_of_fintypeCard_eq, NumberField.canonicalEmbedding.nnnorm_eq, SupIndep.le_sup_iff, BooleanSubalgebra.mem_closure_iff_sup_sdiff, sup_eq_biUnion, ENNReal.coe_finset_sup, Pi.norm_def, IsRetrocompact.finsetSup, image_subset_Iic_sup, ContinuousWithinAt.finset_sup, MvPolynomial.degrees_sum_le, Seminorm.exists_apply_eq_finset_sup, MvPolynomial.schwartz_zippel_sup_sum, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, supIndep_product_iff, le_sup_iff, sup_sdiff_right, toDual_inf, sup_sub_left, TopologicalSpace.Compacts.coe_finset_sup, TopologicalSpace.CompactOpens.coe_finsetSup, sup_inf, exists_mem_eq_sup, PseudoMetric.IsUltra.finsetSup, Multiset.map_finset_sup, add_sup, nndist_pi_def, IsUltrametricDist.nnnorm_sum_eq_sup_of_pairwise_ne, IsUltrametricDist.nnnorm_prod_eq_sup_of_pairwise_ne, sup_union, SchwartzMap.eLpNorm_le_seminorm, ContinuousAt.finset_sup_apply, BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition, AddSubgroup.FG.finset_sup, supIndep_sigma_iff', sup_map, sup_eq_iSup, isPWO_sup, partiallyWellOrderedOn_sup, MvPolynomial.degreeOf_eq_sup, sup_disjSum, isLUB_sup, Multiset.mem_sup, AddMonoidAlgebra.sup_support_mul_le, sup_singleton_apply, le_sup_of_le, BoxIntegral.Prepartition.distortion_biUnion, TopologicalSpace.Closeds.coe_finset_sup, disjoint_sup_right, inf_sSup_eq_iSup_inf_sup_finset, ContinuousOn.finset_sup, supIndep_iff_disjoint_erase, sup_comm, sup_eq_bot_of_isEmpty, sup_mul_le_mul_sup_of_nonneg, isBoundedUnder_le_finset_sup, sup_image, TopologicalSpace.Clopens.surjective_finset_sup_prod, sup_mem_of_nonempty, ContinuousWithinAt.finset_sup_apply, sup_mono_fun, Multiset.count_finset_sup, Seminorm.zero_or_exists_apply_eq_finset_sup, toDual_sup, sup_sup, TopologicalSpace.Clopens.coe_finset_sup, sup_sdiff_left, Nat.sup_divisors_id, powersetCard_sup, AddMonoidAlgebra.sup_support_pow_le, Nat.cast_finsetSup, Pi.nnnorm_def, Submodule.finite_finset_sup, sup_mem, Seminorm.bound_of_shell_sup, Fintype.exists_disjointed_le, Filter.Tendsto.finset_sup_nhds_apply, sup_congr, sup_mono, sup_neg, sup_ite, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, support_sum_eq, Seminorm.finset_sup_smul, dist_pi_def, Seminorm.isBounded_sup, Polynomial.degree_sum_eq_of_disjoint, apply_sup_le_sum, sup_eq_sSup_image, comp_sup_eq_sup_comp_of_nonempty, disjointed_apply, sup_cons, AddMonoidAlgebra.sup_support_add_le, lt_sup_iff, le_sup_dite_neg, Continuous.finset_sup_apply, SupClosed.finsetSup_mem, sup_eq_zero, nnnorm_sum_le_sup_nnnorm, edist_pi_def, sup_le_iff, sup_himp_right, PseudoMetric.coe_finsetSup, MvPolynomial.totalDegree_finset_sum, sup_inv, sup_apply, limsup_finset_sup, NNReal.finset_sup_mul, sup_inf_sup, wellFoundedOn_sup, sup_divβ‚€, List.foldr_sup_eq_sup_toFinset, sup_def, sup_add_right, sup_div_left, LinearMap.mem_span_iff_bound, WithSeminorms.partial_sups, inf_sdiff_left, sup_add, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, AddMonoidAlgebra.sup_support_finset_prod_le, nnnorm_prod_le_sup_nnnorm, sup_biUnion, sup_bot, Seminorm.ball_finset_sup_eq_iInter, sup_eq_of_isMaxOn, sup_eq_of_max, sym_succ, sup_toFinset, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_pt, sup_mul_left, sup_univ_eq_iSup, sup_imageβ‚‚_le, subset_Iic_sup_id, SupPrime.le_finset_sup, Order.Ideal.finsetSup_mem_iff, Seminorm.ball_finset_sup, sup_sigma, PseudoMetric.finsetSup_apply, MeasureTheory.SimpleFunc.approx_apply, AddSubmonoid.FG.finset_sup, MeasureTheory.IsSetRing.finsetSup_mem, sup'_eq_sup, sup_imageβ‚‚_right, MeasureTheory.SimpleFunc.finset_sup_apply, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_isColimit_desc, SeminormFamily.basisSets_mem, Finpartition.sup_parts, sup_eq_bot_iff, SeminormFamily.basisSets_iff, sup_id_eq_sSup, sup_himp_left, Finpartition.sum_combine, exists_sup_eq_iSup, SchwartzMap.one_add_le_sup_seminorm_apply, sup_id_set_eq_sUnion, ofDual_sup, Matrix.linfty_opNNNorm_def, WithSeminorms.hasBasis_ball, Seminorm.finset_sup_le_sum, sup_add_left, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, Seminorm.finset_sup_apply_le, mul_supβ‚€, sup_mul_right, Seminorm.closedBall_finset_sup_eq_iInter, Matrix.linfty_opNorm_def, sup_mulβ‚€, Matrix.norm_eq_sup_sup_nnnorm, sup_of_mem, WithSeminorms.hasBasis_zero_ball, le_sup, NNReal.finset_sup_div, sup_imageβ‚‚_left, WithSeminorms.finset_sups, AddMonoidAlgebra.supDegree_sum_le, map_finset_sup
sup' πŸ“–CompOp
112 mathmath: sup'_mul_le_mul_sup'_of_nonneg, partialSups_apply, Nonempty.norm_sum_le_sup'_norm, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, sup'_add', sup'_product_left, sup'_imageβ‚‚_left, le_sup'_iff, MeasureTheory.smul_le_stoppedValue_hittingBtwn, measurable_range_sup'', partialSups_eq_sup'_range, IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean, lt_sup'_iff, sup'_Iic, le_sup'_of_le, prodMk_sup'_sup', sup'_prodMap, sup'_mem, ContinuousAt.finset_sup', Continuous.finset_sup'_apply, sup'_image, isBoundedUnder_le_finset_sup', map_finset_sup', sup'_mono, sup'_const, sup'_apply, sup'_inf_distrib_right, truncatedSup_of_mem, sup'_singleton, sup'_mulβ‚€, sup'_pow, ContinuousOn.finset_sup', sup'_lt_iff, Nat.cast_finsetSup', sup'_mono_fun, coe_sup', sup'_eq_csSup_image, max'_eq_sup', sup'_insert, toDual_inf', ofDual_sup', measurable_range_sup', comp_sup'_eq_sup'_comp, sup'_eq_of_forall, sup'_comp_eq_map, sup'_inf_sup', MeasureTheory.smul_le_stoppedValue_hitting, SupClosed.finsetSup'_mem, IsUltrametricDist.norm_sum_eq_sup'_of_pairwise_ne, sup'_le_iff, ContinuousOn.finset_sup'_apply, Filter.Tendsto.finset_sup'_nhds, Polynomial.supNorm_def', sup'_comm, sup'_zero, isLUB_sup', nsmul_sup', sup'_map, centerMass_le_sup, sup'_le, mem_sup', IsRetrocompact.finsetSup', add_sup', Continuous.finset_sup', ContinuousMap.coe_sup', sup'_add, sup'_inf_distrib_left, ContinuousAt.finset_sup'_apply, mul_sup', sup'_induction, Nonempty.norm_prod_le_sup'_norm, Filter.Tendsto.finset_sup'_nhds_apply, ConvexOn.le_sup_of_mem_convexHull, exists_mem_eq_sup', sup'_id_eq_csSup, IsUltrametricDist.norm_prod_eq_sup'_of_pairwise_ne, sup'_cons, MeasureTheory.maximal_ineq, sup'_neg, PseudoMetric.coe_finsetSup, sup'_comp_eq_image, sup'_union, ofDual_inf', sup'_imageβ‚‚_le, Seminorm.closedBall_finset_sup', mulβ‚€_sup', isCoboundedUnder_le_finset_sup', ContinuousWithinAt.finset_sup'_apply, measurable_sup', sup'_congr, sup'_one, CompactlySupportedContinuousMap.coe_finsetSup', sup'_product_right, PseudoMetric.finsetSup_apply, limsup_finset_sup', le_sup', sup'_eq_sup, sup'_mul, sup'_divβ‚€, finsetSup'_mem_supClosure, sup'_univ_eq_ciSup, add_sup'', Seminorm.ball_finset_sup', sup'_imageβ‚‚_right, sup'_eq_zero, ContinuousWithinAt.finset_sup', sup'_inv, ContinuousMap.sup'_apply, CompactlySupportedContinuousMap.finsetSup'_apply, NumberField.house_eq_sup', toDual_sup', sup'_biUnion

Theorems

NameKindAssumesProvesValidatesDepends On
codisjoint_inf_left πŸ“–mathematicalβ€”Codisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
inf
β€”disjoint_sup_left
codisjoint_inf_right πŸ“–mathematicalβ€”Codisjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
inf
β€”disjoint_sup_right
coe_inf' πŸ“–mathematicalNonemptyWithTop.some
inf'
inf
WithTop
WithTop.semilatticeInf
WithTop.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”coe_sup'
coe_inf_of_nonempty πŸ“–mathematicalNonemptyWithTop.some
inf
WithTop
WithTop.semilatticeInf
WithTop.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”coe_sup_of_nonempty
coe_sup' πŸ“–mathematicalNonemptyWithBot.some
sup'
sup
WithBot
WithBot.semilatticeSup
WithBot.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”sup'.eq_1
WithBot.coe_unbot
coe_sup_of_nonempty πŸ“–mathematicalNonemptyWithBot.some
sup
WithBot
WithBot.semilatticeSup
WithBot.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”sup'_eq_sup
coe_sup'
comp_inf'_eq_inf'_comp πŸ“–mathematicalNonempty
SemilatticeInf.toMin
inf'β€”comp_sup'_eq_sup'_comp
comp_inf_eq_inf_comp πŸ“–mathematicalSemilatticeInf.toMin
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
infβ€”comp_sup_eq_sup_comp
comp_inf_eq_inf_comp_of_is_total πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
infβ€”comp_inf_eq_inf_comp
Monotone.map_inf
comp_sup'_eq_sup'_comp πŸ“–mathematicalNonempty
SemilatticeSup.toMax
sup'β€”Nonempty.cons_induction
singleton_nonempty
sup'_congr
cons_nonempty
sup'_cons
comp_sup_eq_sup_comp πŸ“–mathematicalSemilatticeSup.toMax
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
supβ€”cons_induction_on
sup_cons
comp_sup_eq_sup_comp_of_is_total πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toPartialOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
sup
Lattice.toSemilatticeSup
β€”comp_sup_eq_sup_comp
Monotone.map_sup
comp_sup_eq_sup_comp_of_nonempty πŸ“–mathematicalMonotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
SemilatticeSup.toPartialOrder
Nonempty
sup
Lattice.toSemilatticeSup
β€”sup'_eq_sup
comp_sup'_eq_sup'_comp
Monotone.map_sup
compl_inf πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
inf
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
CoheytingAlgebra.toOrderTop
sup
Lattice.toSemilatticeSup
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
β€”map_finset_inf
OrderIsoClass.toInfTopHomClass
OrderIso.instOrderIsoClass
compl_sup πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
sup
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
inf
Lattice.toSemilatticeInf
CoheytingAlgebra.toOrderTop
β€”map_finset_sup
OrderIsoClass.toSupBotHomClass
OrderIso.instOrderIsoClass
disjoint_sup_left πŸ“–mathematicalβ€”Disjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
sup
Lattice.toSemilatticeSup
β€”sup_inf_distrib_right
disjoint_sup_right πŸ“–mathematicalβ€”Disjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
sup
Lattice.toSemilatticeSup
β€”sup_inf_distrib_left
exists_inf_eq_iInf πŸ“–mathematicalβ€”inf
Lattice.toSemilatticeInf
CompleteLattice.toLattice
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
CompleteLattice.toBoundedOrder
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”exists_sup_eq_iSup
instWellFoundedGTOrderDualOfWellFoundedLT
exists_inf_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”exists_sup_ge
instWellFoundedGTOrderDualOfWellFoundedLT
exists_mem_eq_inf πŸ“–mathematicalNonemptyFinset
instMembership
inf
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”exists_mem_eq_sup
exists_mem_eq_inf' πŸ“–mathematicalNonemptyFinset
instMembership
inf'
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”exists_mem_eq_sup'
exists_mem_eq_sup πŸ“–mathematicalNonemptyFinset
instMembership
sup
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”exists_mem_eq_sup'
sup'_eq_sup
exists_mem_eq_sup' πŸ“–mathematicalNonemptyFinset
instMembership
sup'
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”Nonempty.cons_induction
singleton_nonempty
mem_singleton_self
cons_nonempty
sup'_cons
le_total
mem_cons
sup_eq_left
sup_eq_right
exists_sup_eq_iSup πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
CompleteLattice.toBoundedOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”exists_sup_ge
LE.le.antisymm
sup_le
le_iSup
iSup_le
exists_sup_ge πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”isEmpty_or_nonempty
IsEmpty.instSubsingleton
WellFounded.has_min
wellFounded_gt
Set.range_nonempty
sup_insert
right_lt_sup
inf'_apply πŸ“–mathematicalNonemptyinf'
Pi.instSemilatticeInf
β€”sup'_apply
inf'_comm πŸ“–mathematicalNonemptyinf'β€”sup'_comm
inf'_comp_eq_image πŸ“–mathematicalNonemptyinf'
image
Nonempty.image
β€”sup'_comp_eq_image
inf'_comp_eq_map πŸ“–mathematicalNonemptyinf'
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
map
map_nonempty
β€”sup'_comp_eq_map
inf'_congr πŸ“–mathematicalNonemptyinf'
Finset
β€”sup'_congr
inf'_cons πŸ“–mathematicalNonempty
Finset
instMembership
inf'
cons
cons_nonempty
SemilatticeInf.toMin
β€”sup'_cons
inf'_const πŸ“–mathematicalNonemptyinf'β€”sup'_const
inf'_eq_inf πŸ“–mathematicalNonemptyinf'
inf
β€”sup'_eq_sup
inf'_eq_of_forall πŸ“–mathematicalNonemptyinf'β€”sup'_eq_of_forall
inf'_image πŸ“–mathematicalNonempty
image
inf'
Nonempty.of_image
β€”sup'_image
inf'_induction πŸ“–mathematicalNonempty
SemilatticeInf.toMin
inf'β€”sup'_induction
inf'_insert πŸ“–mathematicalNonemptyinf'
Finset
instInsert
insert_nonempty
SemilatticeInf.toMin
β€”sup'_insert
inf'_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf'
β€”le_sup'
inf'_le_iff πŸ“–mathematicalNonemptyPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
inf'
Finset
instMembership
β€”le_sup'_iff
inf'_le_of_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf'β€”LE.le.trans
inf'_le
inf'_lt_iff πŸ“–mathematicalNonemptyPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
inf'
Finset
instMembership
β€”lt_sup'_iff
inf'_map πŸ“–mathematicalNonempty
map
inf'
map_nonempty
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
β€”sup'_map
inf'_mem πŸ“–mathematicalSet
Set.instMembership
SemilatticeInf.toMin
Nonempty
inf'β€”inf'_induction
inf'_mono πŸ“–mathematicalFinset
instHasSubset
Nonempty
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf'
Nonempty.mono
β€”le_inf'
Nonempty.mono
inf'_le
inf'_singleton πŸ“–mathematicalβ€”inf'
Finset
instSingleton
singleton_nonempty
β€”singleton_nonempty
inf'_sup_distrib_left πŸ“–mathematicalNonemptySemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
inf'
Lattice.toSemilatticeInf
β€”sup'_inf_distrib_left
inf'_sup_distrib_right πŸ“–mathematicalNonemptySemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
inf'
Lattice.toSemilatticeInf
β€”sup'_inf_distrib_right
inf'_union πŸ“–mathematicalNonemptyinf'
Finset
instUnion
Nonempty.mono
subset_union_left
SemilatticeInf.toMin
β€”sup'_union
inf_apply πŸ“–mathematicalβ€”inf
Pi.instSemilatticeInf
Pi.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”sup_apply
inf_attach πŸ“–mathematicalβ€”inf
Finset
instMembership
attach
β€”sup_attach
inf_coe πŸ“–mathematicalTop.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
inf
Subtype.semilatticeInf
Subtype.orderTop
β€”sup_coe
inf_comm πŸ“–mathematicalβ€”infβ€”sup_comm
inf_congr πŸ“–mathematicalβ€”infβ€”fold_congr
instCommutativeMin_mathlib
instAssociativeMin_mathlib
inf_cons πŸ“–mathematicalFinset
instMembership
inf
cons
SemilatticeInf.toMin
β€”sup_cons
inf_const πŸ“–mathematicalNonemptyinfβ€”sup_const
inf_def πŸ“–mathematicalβ€”inf
Multiset.inf
Multiset.map
val
β€”β€”
inf_disjSum πŸ“–mathematicalβ€”inf
disjSum
SemilatticeInf.toMin
β€”instCommutativeMin_mathlib
instAssociativeMin_mathlib
top_inf_eq
fold_disjSum
inf_dite_neg_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”inf_le
inf_dite_pos_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”inf_le
inf_empty πŸ“–mathematicalβ€”inf
Finset
instEmptyCollection
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”β€”
inf_eq_bot_iff πŸ“–mathematicalβ€”inf
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
Finset
instMembership
β€”sup_eq_top_iff
OrderDual.instNontrivial
inf_eq_iInf πŸ“–mathematicalβ€”inf
Lattice.toSemilatticeInf
CompleteLattice.toLattice
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
CompleteLattice.toBoundedOrder
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Finset
instMembership
β€”sup_eq_iSup
inf_eq_sInf_image πŸ“–mathematicalβ€”inf
Lattice.toSemilatticeInf
CompleteLattice.toLattice
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
CompleteLattice.toBoundedOrder
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set.image
SetLike.coe
Finset
instSetLike
β€”sup_eq_sSup_image
inf_eq_top_iff πŸ“–mathematicalβ€”inf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”sup_eq_bot_iff
inf_erase_top πŸ“–mathematicalβ€”inf
erase
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”sup_erase_bot
inf_himp_right πŸ“–mathematicalβ€”inf
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
CoheytingAlgebra.toOrderTop
HImp.himp
BooleanAlgebra.toHImp
sup
Lattice.toSemilatticeSup
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
β€”sup_sdiff_left
inf_id_eq_sInf πŸ“–mathematicalβ€”inf
Lattice.toSemilatticeInf
CompleteLattice.toLattice
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
CompleteLattice.toBoundedOrder
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
SetLike.coe
Finset
instSetLike
β€”sup_id_eq_sSup
inf_id_set_eq_sInter πŸ“–mathematicalβ€”inf
Set
Lattice.toSemilatticeInf
CompleteLattice.toLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instOrderTop
Set.sInter
SetLike.coe
Finset
instSetLike
β€”inf_id_eq_sInf
inf_image πŸ“–mathematicalβ€”inf
image
β€”fold_image_idem
instCommutativeMin_mathlib
instAssociativeMin_mathlib
instIdempotentOpMin_mathlib
inf_induction πŸ“–mathematicalTop.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
infβ€”sup_induction
inf_inf πŸ“–mathematicalβ€”inf
Pi.instMinForall_mathlib
SemilatticeInf.toMin
β€”sup_sup
inf_insert πŸ“–mathematicalβ€”inf
Finset
instInsert
SemilatticeInf.toMin
β€”fold_insert_idem
instCommutativeMin_mathlib
instAssociativeMin_mathlib
instIdempotentOpMin_mathlib
inf_ite πŸ“–mathematicalβ€”inf
SemilatticeInf.toMin
filter
β€”fold_ite
instCommutativeMin_mathlib
instAssociativeMin_mathlib
instIdempotentOpMin_mathlib
inf_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”le_inf_iff
le_rfl
inf_le_iff πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
inf
Finset
instMembership
β€”le_sup_iff
inf_le_of_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
infβ€”LE.le.trans
inf_le
inf_lt_iff πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
inf
Finset
instMembership
β€”lt_sup_iff
inf_map πŸ“–mathematicalβ€”inf
map
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
β€”fold_map
instCommutativeMin_mathlib
instAssociativeMin_mathlib
inf_mem πŸ“–mathematicalSet
Set.instMembership
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
SemilatticeInf.toMin
infβ€”inf_induction
inf_mono πŸ“–mathematicalFinset
instHasSubset
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”le_inf
inf_le
inf_mono_fun πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
infβ€”le_inf
le_trans
inf_le
inf_of_mem πŸ“–mathematicalFinset
instMembership
inf
WithTop
WithTop.semilatticeInf
WithTop.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
WithTop.some
β€”sup_of_mem
inf_sdiff_left πŸ“–mathematicalNonemptyinf
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
CoheytingAlgebra.toOrderTop
BooleanAlgebra.toSDiff
sup
Lattice.toSemilatticeSup
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
β€”Nonempty.cons_induction
sup_singleton
inf_singleton
sup_cons
inf_cons
sdiff_sup
inf_sdiff_right πŸ“–mathematicalNonemptyinf
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
CoheytingAlgebra.toOrderTop
BooleanAlgebra.toSDiff
β€”Nonempty.cons_induction
inf_singleton
inf_cons
inf_sdiff
inf_set_eq_iInter πŸ“–mathematicalβ€”inf
Set
Lattice.toSemilatticeInf
CompleteLattice.toLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instOrderTop
Set.iInter
Finset
instMembership
β€”inf_eq_iInf
inf_singleton πŸ“–mathematicalβ€”inf
Finset
instSingleton
β€”Multiset.inf_singleton
inf_sup_distrib_left πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
inf
Lattice.toSemilatticeInf
β€”sup_inf_distrib_left
inf_sup_distrib_right πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
inf
Lattice.toSemilatticeInf
β€”sup_inf_distrib_right
inf_top πŸ“–mathematicalβ€”inf
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”sup_bot
inf_union πŸ“–mathematicalβ€”inf
Finset
instUnion
SemilatticeInf.toMin
β€”eq_of_forall_le_iff
isGLB_inf πŸ“–mathematicalβ€”IsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Set.image
SetLike.coe
Finset
instSetLike
inf
β€”β€”
isGLB_inf' πŸ“–mathematicalNonemptyIsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
SetLike.coe
Finset
instSetLike
inf'
β€”inf'_le
le_inf'
isGLB_inf_id πŸ“–mathematicalβ€”IsGLB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
SetLike.coe
Finset
instSetLike
inf
β€”Set.image_congr
Set.image_id'
isGLB_inf
isLUB_sup πŸ“–mathematicalβ€”IsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Set.image
SetLike.coe
Finset
instSetLike
sup
β€”β€”
isLUB_sup' πŸ“–mathematicalNonemptyIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
SetLike.coe
Finset
instSetLike
sup'
β€”le_sup'
sup'_le
isLUB_sup_id πŸ“–mathematicalβ€”IsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
SetLike.coe
Finset
instSetLike
sup
β€”Set.image_congr
Set.image_id'
isLUB_sup
le_inf πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
infβ€”le_inf_iff
le_inf' πŸ“–mathematicalNonempty
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf'β€”sup'_le
le_inf'_iff πŸ“–mathematicalNonemptyPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf'
β€”sup'_le_iff
le_inf_const_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”le_inf
le_rfl
le_inf_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”sup_le_iff
le_sup πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”sup_le_iff
le_rfl
le_sup' πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup'
β€”sup'_le_iff
le_rfl
le_sup'_iff πŸ“–mathematicalNonemptyPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
sup'
Lattice.toSemilatticeSup
Finset
instMembership
β€”WithBot.coe_le_coe
coe_sup'
le_sup_iff
WithBot.bot_lt_coe
le_sup'_of_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup'β€”LE.le.trans
le_sup'
le_sup_dite_neg πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”β€”
le_sup_dite_pos πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”β€”
le_sup_iff πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
sup
Lattice.toSemilatticeSup
Finset
instMembership
β€”cons_induction
not_le_of_gt
sup_cons
le_sup_iff
mem_cons
le_trans
le_sup
le_sup_of_le πŸ“–mathematicalFinset
instMembership
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
supβ€”LE.le.trans
le_sup
lt_inf'_iff πŸ“–mathematicalNonemptyPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
inf'
β€”sup'_lt_iff
lt_inf_iff πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Top.top
OrderTop.toTop
Preorder.toLE
infβ€”sup_lt_iff
lt_sup'_iff πŸ“–mathematicalNonemptyPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
sup'
Lattice.toSemilatticeSup
Finset
instMembership
β€”WithBot.coe_lt_coe
coe_sup'
lt_sup_iff
lt_sup_iff πŸ“–mathematicalβ€”Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
sup
Lattice.toSemilatticeSup
Finset
instMembership
β€”cons_induction
not_lt_bot
sup_cons
lt_sup_iff
mem_cons
lt_of_lt_of_le
le_sup
mem_inf' πŸ“–mathematicalNonemptyFinset
instMembership
inf'
Lattice.toSemilatticeInf
instLattice
β€”Nonempty.cons_induction
cons_nonempty
inf'_cons
mem_sup πŸ“–mathematicalβ€”Finset
instMembership
sup
Lattice.toSemilatticeSup
instLattice
instOrderBot
β€”cons_induction
sup_empty
sup_cons
mem_sup' πŸ“–mathematicalNonemptyFinset
instMembership
sup'
Lattice.toSemilatticeSup
instLattice
β€”Nonempty.cons_induction
cons_nonempty
sup'_cons
ofDual_inf πŸ“–mathematicalβ€”DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
inf
OrderDual.instSemilatticeInf
OrderDual.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”β€”
ofDual_inf' πŸ“–mathematicalNonemptyDFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
inf'
OrderDual.instSemilatticeInf
sup'
β€”β€”
ofDual_sup πŸ“–mathematicalβ€”DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
sup
OrderDual.instSemilatticeSup
OrderDual.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
inf
β€”β€”
ofDual_sup' πŸ“–mathematicalNonemptyDFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
sup'
OrderDual.instSemilatticeSup
inf'
β€”β€”
subset_range_sup_succ πŸ“–mathematicalβ€”Finset
instHasSubset
range
sup
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeNat
Nat.instOrderBot
β€”mem_range
le_sup
sup'_apply πŸ“–mathematicalNonemptysup'
Pi.instSemilatticeSup
β€”comp_sup'_eq_sup'_comp
sup'_comm πŸ“–mathematicalNonemptysup'β€”eq_of_forall_ge_iff
forallβ‚‚_swap
sup'_comp_eq_image πŸ“–mathematicalNonemptysup'
image
Nonempty.image
β€”Nonempty.image
sup'_image
sup'_comp_eq_map πŸ“–mathematicalNonemptysup'
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
map
map_nonempty
β€”map_nonempty
sup'_map
sup'_congr πŸ“–mathematicalNonemptysup'
Finset
β€”eq_of_forall_ge_iff
sup'_cons πŸ“–mathematicalNonempty
Finset
instMembership
sup'
cons
cons_nonempty
SemilatticeSup.toMax
β€”cons_nonempty
WithBot.coe_eq_coe
coe_sup'
sup_cons
sup'_const πŸ“–mathematicalNonemptysup'β€”sup'_eq_of_forall
sup'_eq_of_forall πŸ“–mathematicalNonemptysup'β€”le_antisymm
sup'_le
Eq.le
le_sup'_of_le
Eq.ge
sup'_eq_sup πŸ“–mathematicalNonemptysup'
sup
β€”le_antisymm
sup'_le
le_sup
sup_le
le_sup'
sup'_image πŸ“–mathematicalNonempty
image
sup'
Nonempty.of_image
β€”Nonempty.of_image
WithBot.coe_eq_coe
coe_sup'
sup_image
sup'_induction πŸ“–mathematicalNonempty
SemilatticeSup.toMax
sup'β€”coe_sup'
sup_induction
bot_sup_eq
sup_bot_eq
sup'_inf_distrib_left πŸ“–mathematicalNonemptySemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
sup'
Lattice.toSemilatticeSup
β€”Nonempty.cons_induction
cons_nonempty
sup'_cons
inf_sup_left
sup'_inf_distrib_right πŸ“–mathematicalNonemptySemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
sup'
Lattice.toSemilatticeSup
β€”inf_comm
sup'_inf_distrib_left
sup'_congr
sup'_insert πŸ“–mathematicalNonemptysup'
Finset
instInsert
insert_nonempty
SemilatticeSup.toMax
β€”insert_nonempty
WithBot.coe_eq_coe
coe_sup'
sup_insert
sup'_le πŸ“–mathematicalNonempty
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup'β€”sup'_le_iff
sup'_le_iff πŸ“–mathematicalNonemptyPreorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup'
β€”WithBot.coe_le_coe
coe_sup'
sup'_lt_iff πŸ“–mathematicalNonemptyPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
sup'
Lattice.toSemilatticeSup
β€”WithBot.coe_lt_coe
coe_sup'
sup_lt_iff
WithBot.bot_lt_coe
sup'_map πŸ“–mathematicalNonempty
map
sup'
map_nonempty
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
β€”map_nonempty
WithBot.coe_eq_coe
coe_sup'
sup_map
sup'_mem πŸ“–mathematicalSet
Set.instMembership
SemilatticeSup.toMax
Nonempty
sup'β€”sup'_induction
sup'_mono πŸ“–mathematicalFinset
instHasSubset
Nonempty
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup'
Nonempty.mono
β€”sup'_le
Nonempty.mono
le_sup'
sup'_mono_fun πŸ“–mathematicalNonempty
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup'β€”sup'_le
LE.le.trans
le_sup'
sup'_singleton πŸ“–mathematicalβ€”sup'
Finset
instSingleton
singleton_nonempty
β€”singleton_nonempty
sup'_union πŸ“–mathematicalNonemptysup'
Finset
instUnion
Nonempty.mono
subset_union_left
SemilatticeSup.toMax
β€”eq_of_forall_ge_iff
Nonempty.mono
subset_union_left
sup_apply πŸ“–mathematicalβ€”sup
Pi.instSemilatticeSup
Pi.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”comp_sup_eq_sup_comp
sup_attach πŸ“–mathematicalβ€”sup
Finset
instMembership
attach
β€”sup_map
instCommutativeMax_mathlib
instAssociativeMax_mathlib
attach_map_val
sup_bot πŸ“–mathematicalβ€”sup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”eq_empty_or_nonempty
sup_empty
sup_const
sup_coe πŸ“–mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
sup
Subtype.semilatticeSup
Subtype.orderBot
β€”comp_sup_eq_sup_comp
sup_comm πŸ“–mathematicalβ€”supβ€”eq_of_forall_ge_iff
forallβ‚‚_swap
sup_congr πŸ“–mathematicalβ€”supβ€”fold_congr
instCommutativeMax_mathlib
instAssociativeMax_mathlib
sup_cons πŸ“–mathematicalFinset
instMembership
sup
cons
SemilatticeSup.toMax
β€”fold_cons
instCommutativeMax_mathlib
instAssociativeMax_mathlib
sup_const πŸ“–mathematicalNonemptysupβ€”eq_of_forall_ge_iff
sup_le_iff
Nonempty.forall_const
sup_const_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”sup_le
le_rfl
sup_def πŸ“–mathematicalβ€”sup
Multiset.sup
Multiset.map
val
β€”β€”
sup_disjSum πŸ“–mathematicalβ€”sup
disjSum
SemilatticeSup.toMax
β€”instCommutativeMax_mathlib
instAssociativeMax_mathlib
bot_sup_eq
fold_disjSum
sup_empty πŸ“–mathematicalβ€”sup
Finset
instEmptyCollection
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”fold_empty
instCommutativeMax_mathlib
instAssociativeMax_mathlib
sup_eq_bot_iff πŸ“–mathematicalβ€”sup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”induction
sup_empty
instIsEmptyFalse
sup_insert
sup_eq_bot_of_isEmpty πŸ“–mathematicalβ€”sup
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”sup_eq_bot_iff
IsEmpty.false
sup_eq_iSup πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
CompleteLattice.toBoundedOrder
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Finset
instMembership
β€”le_antisymm
sup_le
le_iSup_of_le
le_iSup
iSup_le
le_sup
sup_eq_sSup_image πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
CompleteLattice.toBoundedOrder
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.image
SetLike.coe
Finset
instSetLike
β€”coe_image
sup_id_eq_sSup
sup_image
sup_eq_top_iff πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Top.top
OrderTop.toTop
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderTop
Finset
instMembership
β€”le_sup_iff
bot_lt_top
sup_erase_bot πŸ“–mathematicalβ€”sup
erase
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”LE.le.antisymm
sup_mono
erase_subset
sup_le_iff
eq_or_ne
bot_le
le_sup
mem_erase
sup_himp_left πŸ“–mathematicalNonemptysup
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
HImp.himp
BooleanAlgebra.toHImp
β€”inf_sdiff_right
sup_himp_right πŸ“–mathematicalNonemptysup
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
HImp.himp
BooleanAlgebra.toHImp
inf
Lattice.toSemilatticeInf
CoheytingAlgebra.toOrderTop
β€”inf_sdiff_left
sup_id_eq_sSup πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
CompleteLattice.toBoundedOrder
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SetLike.coe
Finset
instSetLike
β€”sup_eq_iSup
iSup_congr_Prop
sSup_eq_iSup
sup_id_set_eq_sUnion πŸ“–mathematicalβ€”sup
Set
Lattice.toSemilatticeSup
CompleteLattice.toLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Set.sUnion
SetLike.coe
Finset
instSetLike
β€”sup_id_eq_sSup
sup_image πŸ“–mathematicalβ€”sup
image
β€”fold_image_idem
instCommutativeMax_mathlib
instAssociativeMax_mathlib
instIdempotentOpMax_mathlib
sup_induction πŸ“–mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
supβ€”cons_induction
sup_cons
sup_inf_distrib_left πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
sup
Lattice.toSemilatticeSup
β€”cons_induction
sup_empty
inf_bot_eq
sup_cons
inf_sup_left
sup_inf_distrib_right πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
sup
Lattice.toSemilatticeSup
β€”inf_comm
sup_inf_distrib_left
sup_insert πŸ“–mathematicalβ€”sup
Finset
instInsert
SemilatticeSup.toMax
β€”fold_insert_idem
instCommutativeMax_mathlib
instAssociativeMax_mathlib
instIdempotentOpMax_mathlib
sup_ite πŸ“–mathematicalβ€”sup
SemilatticeSup.toMax
filter
β€”fold_ite
instCommutativeMax_mathlib
instAssociativeMax_mathlib
instIdempotentOpMax_mathlib
sup_le πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
supβ€”sup_le_iff
sup_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”Multiset.sup_le
sup_le_of_le_directed πŸ“–mathematicalSet.Nonempty
DirectedOn
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Set
Set.instMembership
supβ€”induction_on
sup_empty
coe_subset
subset_insert
mem_insert_self
sup_insert
sup_le_iff
le_trans
sup_lt_iff πŸ“–mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Bot.bot
OrderBot.toBot
Preorder.toLE
sup
Lattice.toSemilatticeSup
β€”lt_of_le_of_lt
le_sup
cons_induction_on
sup_cons
sup_map πŸ“–mathematicalβ€”sup
map
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
β€”fold_map
instCommutativeMax_mathlib
instAssociativeMax_mathlib
sup_mem πŸ“–mathematicalSet
Set.instMembership
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
SemilatticeSup.toMax
supβ€”sup_induction
sup_mem_of_nonempty πŸ“–mathematicalNonemptySet
Set.instMembership
Set.image
SetLike.coe
Finset
instSetLike
sup
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
β€”induction
sup_insert
eq_empty_or_nonempty
instLawfulSingleton
coe_singleton
Set.image_singleton
sup_empty
sup_of_le_left
coe_insert
le_total
sup_eq_right
Set.image_mono
Set.subset_insert
sup_eq_left
Set.mem_image_of_mem
Set.mem_insert
sup_mono πŸ“–mathematicalFinset
instHasSubset
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
sup
β€”sup_le
le_sup
sup_mono_fun πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
supβ€”sup_le
le_trans
le_sup
sup_of_mem πŸ“–mathematicalFinset
instMembership
sup
WithBot
WithBot.semilatticeSup
WithBot.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
WithBot.some
β€”WithBot.le_iff_forall
le_sup
sup_sdiff_left πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
BooleanAlgebra.toSDiff
inf
Lattice.toSemilatticeInf
CoheytingAlgebra.toOrderTop
β€”cons_induction
sup_empty
inf_empty
sdiff_top
sup_cons
inf_cons
sdiff_inf
sup_sdiff_right πŸ“–mathematicalβ€”sup
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra
GeneralizedBooleanAlgebra.toOrderBot
GeneralizedBooleanAlgebra.toSDiff
β€”cons_induction
sup_empty
bot_sdiff
sup_cons
sup_sdiff
sup_set_eq_biUnion πŸ“–mathematicalβ€”sup
Set
Lattice.toSemilatticeSup
CompleteLattice.toLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Set.iUnion
Finset
instMembership
β€”sup_eq_iSup
sup_singleton πŸ“–mathematicalβ€”sup
Finset
instSingleton
β€”Multiset.sup_singleton
sup_singleton_apply πŸ“–mathematicalβ€”sup
Finset
Lattice.toSemilatticeSup
instLattice
instOrderBot
instSingleton
image
β€”ext
mem_sup
mem_image
sup_singleton_eq_self πŸ“–mathematicalβ€”sup
Finset
Lattice.toSemilatticeSup
instLattice
instOrderBot
instSingleton
β€”sup_singleton_apply
image_id
sup_sup πŸ“–mathematicalβ€”sup
Pi.instMaxForall_mathlib
SemilatticeSup.toMax
β€”cons_induction
sup_empty
bot_sup_eq
sup_cons
sup_sup_sup_comm
sup_toFinset πŸ“–mathematicalβ€”Multiset.toFinset
sup
Multiset
Lattice.toSemilatticeSup
Multiset.instLattice
Multiset.instOrderBot
Finset
instLattice
instOrderBot
β€”comp_sup_eq_sup_comp
Multiset.toFinset_union
sup_union πŸ“–mathematicalβ€”sup
Finset
instUnion
SemilatticeSup.toMax
β€”eq_of_forall_ge_iff
toDual_inf πŸ“–mathematicalβ€”DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
inf
sup
OrderDual.instSemilatticeSup
OrderDual.instOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
β€”β€”
toDual_inf' πŸ“–mathematicalNonemptyDFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
inf'
sup'
OrderDual.instSemilatticeSup
β€”β€”
toDual_sup πŸ“–mathematicalβ€”DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
sup
inf
OrderDual.instSemilatticeInf
OrderDual.instOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
β€”β€”
toDual_sup' πŸ“–mathematicalNonemptyDFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
sup'
inf'
OrderDual.instSemilatticeInf
β€”β€”

Finset.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
inf_eq_bot_iff πŸ“–mathematicalFinset.NonemptyFinset.inf
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
Finset
Finset.instMembership
β€”sup_eq_top_iff
sup_eq_top_iff πŸ“–mathematicalFinset.NonemptyFinset.sup
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
BoundedOrder.toOrderBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Top.top
OrderTop.toTop
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
BoundedOrder.toOrderTop
Finset
Finset.instMembership
β€”subsingleton_or_nontrivial
Finset.sup_eq_top_iff

List

Theorems

NameKindAssumesProvesValidatesDepends On
foldr_inf_eq_inf_toFinset πŸ“–mathematicalβ€”SemilatticeInf.toMin
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Finset.inf
toFinset
β€”instCommutativeMin_mathlib
instAssociativeMin_mathlib
Multiset.coe_fold_r
Multiset.fold_dedup_idem
instIdempotentOpMin_mathlib
Finset.inf_def
toFinset_coe
Multiset.toFinset_val
Multiset.map_id
foldr_sup_eq_sup_toFinset πŸ“–mathematicalβ€”SemilatticeSup.toMax
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Finset.sup
toFinset
β€”instCommutativeMax_mathlib
instAssociativeMax_mathlib
Multiset.coe_fold_r
Multiset.fold_dedup_idem
instIdempotentOpMax_mathlib
Finset.sup_def
toFinset_coe
Multiset.toFinset_val
Multiset.map_id

Multiset

Theorems

NameKindAssumesProvesValidatesDepends On
count_finset_sup πŸ“–mathematicalβ€”count
Finset.sup
Multiset
Lattice.toSemilatticeSup
instLattice
instOrderBot
DistribLattice.toLattice
instDistribLatticeNat
Nat.instOrderBot
β€”Finset.induction
count_zero
Finset.sup_insert
sup_eq_union
count_union
map_finset_sup πŸ“–mathematicalβ€”map
Finset.sup
Multiset
Lattice.toSemilatticeSup
instLattice
instOrderBot
β€”Finset.comp_sup_eq_sup_comp
map_union
map_zero
mem_sup πŸ“–mathematicalβ€”Multiset
instMembership
Finset.sup
Lattice.toSemilatticeSup
instLattice
instOrderBot
Finset
Finset.instMembership
β€”Finset.cons_induction
Finset.sup_empty
Finset.sup_cons

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
map_finset_inf πŸ“–mathematicalβ€”DFunLike.coe
Finset.inf
β€”Finset.cons_induction_on
TopHomClass.map_top
InfTopHomClass.toTopHomClass
Finset.inf_cons
InfHomClass.map_inf
InfTopHomClass.toInfHomClass
map_finset_inf' πŸ“–mathematicalFinset.NonemptyDFunLike.coe
Finset.inf'
β€”Finset.Nonempty.cons_induction
Finset.singleton_nonempty
Finset.inf'_congr
Finset.cons_nonempty
Finset.inf'_cons
InfHomClass.map_inf
map_finset_sup πŸ“–mathematicalβ€”DFunLike.coe
Finset.sup
β€”Finset.cons_induction_on
BotHomClass.map_bot
SupBotHomClass.toBotHomClass
Finset.sup_cons
SupHomClass.map_sup
SupBotHomClass.toSupHomClass
map_finset_sup' πŸ“–mathematicalFinset.NonemptyDFunLike.coe
Finset.sup'
β€”Finset.Nonempty.cons_induction
Finset.singleton_nonempty
Finset.sup'_congr
Finset.cons_nonempty
Finset.sup'_cons
SupHomClass.map_sup

---

← Back to Index