Documentation Verification Report

Pi

📁 Source: Mathlib/Topology/MetricSpace/Pseudo/Pi.lean

Statistics

MetricCount
DefinitionspseudoMetricSpacePi
1
Theoremsdist_insertNth_insertNth, nndist_insertNth_insertNth, ball_pi, ball_pi', closedBall_pi, closedBall_pi', dist_le_pi_dist, dist_pi_const, dist_pi_const_le, dist_pi_def, dist_pi_eq_iff, dist_pi_le_iff, dist_pi_le_iff', dist_pi_lt_iff, dist_single_single, nndist_le_pi_nndist, nndist_pi_const, nndist_pi_const_le, nndist_pi_def, nndist_pi_eq_iff, nndist_pi_le_iff, nndist_pi_lt_iff, nndist_single_single, sphere_pi
24
Total25

Fin

Theorems

NameKindAssumesProvesValidatesDepends On
dist_insertNth_insertNth 📖mathematicalDist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
fintype
insertNth
Real
Real.instMax
succAbove
nndist_insertNth_insertNth
NNReal.coe_max
nndist_insertNth_insertNth 📖mathematicalNNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
fintype
insertNth
NNReal
NNReal.instMax
succAbove
eq_of_forall_ge_iff
forall_iff_succAbove
insertNth_apply_same
insertNth_apply_succAbove

(root)

Definitions

NameCategoryTheorems
pseudoMetricSpacePi 📖CompOp
71 mathmath: Fin.nndist_insertNth_insertNth, nndist_pi_le_iff, Topology.CWComplex.continuousOn, Topology.RelCWComplex.pairwiseDisjoint', IsLowerSet.exists_subset_ball, Real.volume_pi_ball, Topology.RelCWComplex.source_eq, Topology.RelCWComplex.continuousOn, stdSimplex_subset_closedBall, Topology.RelCWComplex.union', diam_stdSimplex, sphere_pi, closedBall_pi', BoxIntegral.Box.nndist_le_distortion_mul, BoxIntegral.TaggedPrepartition.isSubordinate_single, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, pi_properSpace, nndist_le_pi_nndist, Real.dimH_ball_pi, MeasureTheory.Measure.pi_ball, nndist_single_single, Pi.instIsBoundedSMul', nndist_pi_const, diam_stdSimplex_of_subsingleton, BoxIntegral.Box.dist_le_distortion_mul, Topology.CWComplex.union', dist_pi_le_iff, diam_stdSimplex_le, Topology.CWComplex.source_eq, Topology.CWComplex.pairwiseDisjoint', ball_pi, dist_single_single, MeasureTheory.Measure.IsUnifLocDoublingMeasure.volume_pi, dist_pi_lt_iff, Topology.CWComplex.mapsTo', dist_mono_left_pi, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, dist_pi_eq_iff, nndist_pi_const_le, nndist_pi_def, closedBall_pi, Pi.instIsBoundedSMul, Pi.instIsUltrametricDist, MeasureTheory.Measure.pi_closedBall, BoxIntegral.Box.diam_Icc_le_of_distortion_le, MeasureTheory.volume_pi_ball, dist_le_dist_of_le_pi, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, Real.dimH_ball_pi_fin, Real.dist_le_of_mem_pi_Icc, MeasureTheory.volume_pi_closedBall, Topology.RelCWComplex.mapsTo, Topology.RelCWComplex.disjointBase', dist_pi_def, dist_anti_right_pi, IsUpperSet.exists_subset_ball, IsUnifLocDoublingMeasure.pi, dist_pi_const, dist_pi_const_le, Fin.dist_insertNth_insertNth, nndist_pi_lt_iff, dist_mono_right_pi, Topology.CWComplex.mapsTo, BoxIntegral.unitPartition.diam_boxIcc, dist_le_pi_dist, dist_inf_sup_pi, Real.volume_pi_closedBall, dist_pi_le_iff', ball_pi', dist_anti_left_pi, nndist_pi_eq_iff

Theorems

NameKindAssumesProvesValidatesDepends On
ball_pi 📖mathematicalReal
Real.instLT
Real.instZero
Metric.ball
pseudoMetricSpacePi
Set.pi
Set.univ
Set.ext
dist_pi_lt_iff
ball_pi' 📖mathematicalMetric.ball
pseudoMetricSpacePi
Set.pi
Set.univ
lt_or_ge
ball_pi
Metric.ball_eq_empty
Set.univ_pi_empty
closedBall_pi 📖mathematicalReal
Real.instLE
Real.instZero
Metric.closedBall
pseudoMetricSpacePi
Set.pi
Set.univ
Set.ext
dist_pi_le_iff
closedBall_pi' 📖mathematicalMetric.closedBall
pseudoMetricSpacePi
Set.pi
Set.univ
le_or_gt
closedBall_pi
Metric.closedBall_eq_empty
Set.univ_pi_empty
dist_le_pi_dist 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
nndist_le_pi_nndist
dist_pi_const 📖mathematicalDist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
dist_edist
edist_pi_const
dist_pi_const_le 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
dist_pi_le_iff
dist_nonneg
le_rfl
dist_pi_def 📖mathematicalDist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
NNReal.toReal
Finset.sup
NNReal
instSemilatticeSupNNReal
NNReal.instOrderBot
Finset.univ
NNDist.nndist
PseudoMetricSpace.toNNDist
dist_pi_eq_iff 📖mathematicalReal
Real.instLT
Real.instZero
Dist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
Real.instLE
CanLift.prf
NNReal.canLift
LT.lt.le
nndist_pi_eq_iff
dist_pi_le_iff 📖mathematicalReal
Real.instLE
Real.instZero
Dist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
CanLift.prf
NNReal.canLift
nndist_pi_le_iff
dist_pi_le_iff' 📖mathematicalReal
Real.instLE
Dist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
dist_pi_le_iff
LE.le.trans
dist_nonneg
dist_pi_lt_iff 📖mathematicalReal
Real.instLT
Real.instZero
Dist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
CanLift.prf
NNReal.canLift
LT.lt.le
nndist_pi_lt_iff
dist_single_single 📖mathematicalDist.dist
PseudoMetricSpace.toDist
pseudoMetricSpacePi
Pi.single
Real
Real.instMax
nndist_single_single
NNReal.coe_max
nndist_le_pi_nndist 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
ENNReal.coe_le_coe
edist_nndist
edist_le_pi_edist
nndist_pi_const 📖mathematicalNNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
NNReal.eq
dist_pi_const
nndist_pi_const_le 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
nndist_pi_le_iff
le_rfl
nndist_pi_def 📖mathematicalNNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
Finset.sup
NNReal
instSemilatticeSupNNReal
NNReal.instOrderBot
Finset.univ
nndist_pi_eq_iff 📖mathematicalNNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
instZeroNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
Preorder.toLE
eq_iff_le_not_lt
nndist_pi_lt_iff
nndist_pi_le_iff
nndist_pi_le_iff 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
nndist_pi_lt_iff 📖mathematicalNNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
instZeroNNReal
NNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
Finset.sup_lt_iff
nndist_single_single 📖mathematicalNNDist.nndist
PseudoMetricSpace.toNNDist
pseudoMetricSpacePi
Pi.single
NNReal
NNReal.instMax
le_antisymm
nndist_pi_le_iff
Pi.single_apply
nndist_comm
nndist_self
NNReal.instCanonicallyOrderedAdd
max_le
Pi.single_eq_same
Pi.single_eq_of_ne
nndist_le_pi_nndist
Pi.single_eq_of_ne'
sphere_pi 📖mathematicalReal
Real.instLT
Real.instZero
Metric.sphere
pseudoMetricSpacePi
Set
Set.instInter
Set.iUnion
Set.preimage
Function.eval
Metric.closedBall
lt_trichotomy
Metric.sphere_eq_empty_of_neg
Set.iUnion_empty
Metric.closedBall_of_neg
Set.inter_self
Metric.closedBall_eq_sphere_of_nonpos
le_rfl
Set.inter_eq_right
Set.subset_iUnion_of_subset
lt_irrefl
Eq.le
le_antisymm
dist_pi_le_iff
dist_nonneg
Set.ext
dist_pi_eq_iff
LT.lt.le

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