Documentation Verification Report

ConditionallyCompleteOrder

πŸ“ Source: Mathlib/Data/Int/ConditionallyCompleteOrder.lean

Statistics

MetricCount
DefinitionsinstConditionallyCompleteLinearOrder
1
TheoremscsInf_empty, csInf_eq_leastOfBdd, csInf_eq_least_of_bdd, csInf_mem, csInf_of_not_bddBelow, csInf_of_not_bdd_below, csSup_empty, csSup_eq_greatestOfBdd, csSup_eq_greatest_of_bdd, csSup_mem, csSup_of_not_bddAbove, csSup_of_not_bdd_above
12
Total13

Int

Theorems

NameKindAssumesProvesValidatesDepends On
csInf_empty πŸ“–mathematicalβ€”InfSet.sInf
ConditionallyCompleteLattice.toInfSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
Set
Set.instEmptyCollection
β€”β€”
csInf_eq_leastOfBdd πŸ“–mathematicalSet
Set.instMembership
InfSet.sInf
ConditionallyCompleteLattice.toInfSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
Set
Set.instMembership
leastOfBdd
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForall
Lean.Meta.instFastSubsingletonDecidable
coe_leastOfBdd_eq
csInf_eq_least_of_bdd πŸ“–mathematicalSet
Set.instMembership
InfSet.sInf
ConditionallyCompleteLattice.toInfSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
Set
Set.instMembership
leastOfBdd
β€”csInf_eq_leastOfBdd
csInf_mem πŸ“–mathematicalSet.Nonempty
BddBelow
Set
Set.instMembership
InfSet.sInf
ConditionallyCompleteLattice.toInfSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
β€”β€”
csInf_of_not_bddBelow πŸ“–mathematicalBddBelowInfSet.sInf
ConditionallyCompleteLattice.toInfSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
β€”β€”
csInf_of_not_bdd_below πŸ“–mathematicalBddBelowInfSet.sInf
ConditionallyCompleteLattice.toInfSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
β€”csInf_of_not_bddBelow
csSup_empty πŸ“–mathematicalβ€”SupSet.sSup
ConditionallyCompleteLattice.toSupSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
Set
Set.instEmptyCollection
β€”β€”
csSup_eq_greatestOfBdd πŸ“–mathematicalSet
Set.instMembership
SupSet.sSup
ConditionallyCompleteLattice.toSupSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
Set
Set.instMembership
greatestOfBdd
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForall
Lean.Meta.instFastSubsingletonDecidable
coe_greatestOfBdd_eq
csSup_eq_greatest_of_bdd πŸ“–mathematicalSet
Set.instMembership
SupSet.sSup
ConditionallyCompleteLattice.toSupSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
Set
Set.instMembership
greatestOfBdd
β€”csSup_eq_greatestOfBdd
csSup_mem πŸ“–mathematicalSet.Nonempty
BddAbove
Set
Set.instMembership
SupSet.sSup
ConditionallyCompleteLattice.toSupSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
β€”β€”
csSup_of_not_bddAbove πŸ“–mathematicalBddAboveSupSet.sSup
ConditionallyCompleteLattice.toSupSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
β€”β€”
csSup_of_not_bdd_above πŸ“–mathematicalBddAboveSupSet.sSup
ConditionallyCompleteLattice.toSupSet
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
instConditionallyCompleteLinearOrder
β€”csSup_of_not_bddAbove

(root)

Definitions

NameCategoryTheorems
instConditionallyCompleteLinearOrder πŸ“–CompOp
97 mathmath: tendsto_zero_iff_meromorphicOrderAt_pos, SummationFilter.summable_symmetricIco_of_summable_symmetricIcc, EisensteinSeries.hasSum_e2Summand_symmetricIcc, RootPairing.Base.not_nonneg_iff_neg_of_sum_mem_range_root, SummationFilter.tsum_symmetricIcc_eq_tsum_symmetricIco, Padic.withValUniformEquiv_norm_le_one_iff, tendsto_cobounded_iff_meromorphicOrderAt_neg, Rat.padicValuation_cast, Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, Valuation.IsRankOneDiscrete.valueGroupβ‚€_equiv_withZeroMulInt_restrict_apply_of_surjective, Int.padicValuation_lt_one_iff, SummationFilter.HasProd.hasProd_symmetricIco_of_hasProd_symmetricIcc, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, Int.csInf_mem, RootPairing.coe_chainBotCoeff_eq_sSup, setOf_liouvilleWith_subset_aux, Set.Nonempty.eq_Icc_iff_int, Int.padicValuation_eq_one_iff, RootPairing.setOf_root_add_zsmul_mem_eq_Icc, Int.csInf_eq_least_of_bdd, Rat.padicValuation_self, RootPairing.Base.pos_or_neg_of_sum_smul_root_mem, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Valuation.IsRankOneDiscrete.valueGroupβ‚€_equiv_withZeroMulInt_strictMono, Padic.norm_eq_zpow_log_mulValuation, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, meromorphicOrderAt_add, EisensteinSeries.G2_eq_tsum_symmetricIco, Int.csSup_eq_greatestOfBdd, RootPairing.setOf_root_sub_zsmul_mem_eq_Icc, Int.cofinite_eq, tendsto_intCast_atBot_sup_atTop_cobounded, SummationFilter.multipliable_symmetricIco_of_multipliable_symmetricIcc, SummationFilter.hasSum_symmetricIoc_int_iff, AnalyticAt.meromorphicOrderAt_nonneg, Int.ball_eq_Ioo, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, SummationFilter.hasSum_symmetricIcc_iff, RootPairing.coe_chainTopCoeff_eq_sSup, Padic.mulValuation_toFun, Int.csInf_eq_leastOfBdd, RootPairing.setOf_root_add_zsmul_eq_Icc_of_linearIndependent, Padic.comap_mulValuation_eq_padicValuation, Int.csInf_of_not_bddBelow, tendsto_nhds_iff_meromorphicOrderAt_nonneg, EisensteinSeries.hasSum_e2Summand_symmetricIco, Padic.AddValuation.map_add, meromorphicNFAt_iff_analyticAt_or, HasSum.hasSum_symmetricIco_of_hasSum_symmetricIcc, SummationFilter.multipliable_symmetricIco_of_multiplible_symmetricIcc, RootPairing.Base.not_nonpos_iff_pos_of_sum_mem_range_root, Int.padicValuation_self, SummationFilter.hasProd_symmetricIco_int_iff, SummationFilter.hasSum_symmetricIco_int_iff, SummationFilter.tprod_symmetricIcc_eq_tprod_symmetricIco, ClassGroup.norm_lt, Rat.padicValuation_eq_zero_iff, Int.csSup_of_not_bddAbove, Int.csSup_eq_greatest_of_bdd, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, RootPairing.Base.exists_root_eq_sum_int, RootPairing.root_add_zsmul_mem_range_iff, EisensteinSeries.tendsto_double_sum_S_act, SummationFilter.symmetricIcc_eq_symmetricIoo_int, Int.closedBall_eq_Icc, EisensteinSeries.summable_e2Summand_symmetricIcc, Padic.comap_mulValuation_eq_int_padicValuation, Int.csSup_mem, HasProd.hasProd_symmetricIco_of_hasProd_symmetricIcc, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, Padic.norm_rat_le_one_iff_padicValuation_le_one, EisensteinSeries.summable_e2Summand_symmetricIco, RootPairing.root_sub_zsmul_mem_range_iff, Rat.surjective_padicValuation, SummationFilter.symmetricIcc_eq_map_Icc_nat, tendsto_intCast_atTop_cobounded, SummationFilter.hasProd_symmetricIcc_iff, Int.csSup_of_not_bdd_above, Summable.tendsto_zero_of_even_summable_symmetricIcc, Int.padicValuation_le_one, ClassGroup.norm_le, Int.instIsOrderBornology, ZLattice.sum_piFinset_Icc_rpow_le, tendsto_intCast_atBot_cobounded, Pell.IsFundamental.y_strictMono, SummationFilter.hasProd_symmetricIoc_int_iff, Int.csInf_of_not_bdd_below, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, Int.csSup_empty, Int.padicValuation_eq_zero_iff, ClassGroup.exists_mem_finset_approx', ClassGroup.exists_mem_finsetApprox, Rat.padicValuation_le_one_iff, Int.cobounded_eq, Int.csInf_empty, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq

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