Documentation Verification Report

Metric

📁 Source: Mathlib/Combinatorics/SimpleGraph/Metric.lean

Statistics

MetricCount
Definitionsdist, edist
2
Theoremsdiff_dist_adj, diff_dist_adj, dist_eq_zero_iff, dist_triangle, exists_path_of_dist, exists_walk_length_eq_dist, exists_walk_length_eq_edist, one_lt_dist_of_ne_of_not_adj, pos_dist_of_ne, coe_dist_eq_edist, dist_anti, dist_eq_zero_iff, dist_triangle_left, dist_triangle_right, exists_path_of_dist, exists_walk_length_eq_dist, exists_walk_length_eq_edist, of_dist_ne_zero, one_lt_dist_of_ne_of_not_adj, pos_dist_of_ne, edist_le, exists_adj_adj_not_adj_ne, isPath_of_length_eq_dist, dist_bot, dist_comm, dist_eq_one_iff_adj, dist_eq_sInf, dist_eq_zero_iff_eq_or_not_reachable, dist_eq_zero_of_not_reachable, dist_le, dist_ne_zero_iff_ne_and_reachable, dist_self, dist_top, dist_top_of_ne, edist_anti, edist_bot, edist_bot_of_ne, edist_comm, edist_eq_one_iff_adj, edist_eq_sInf, edist_eq_top_of_not_reachable, edist_eq_zero_iff, edist_le, edist_le_one_iff_adj_or_eq, edist_ne_top_iff_reachable, edist_pos_of_ne, edist_self, edist_top, edist_top_of_ne, edist_triangle, exists_walk_of_dist_ne_zero, exists_walk_of_edist_eq_coe, exists_walk_of_edist_ne_top, length_eq_dist_of_subwalk, nonempty_of_pos_dist, reachable_of_edist_ne_top
56
Total58

SimpleGraph

Definitions

NameCategoryTheorems
dist 📖CompOp
32 mathmath: Reachable.dist_anti, Connected.one_lt_dist_of_ne_of_not_adj, Reachable.one_lt_dist_of_ne_of_not_adj, Connected.dist_triangle, Connected.exists_walk_length_eq_dist, dist_eq_sInf, dist_comm, dist_le_diam, dist_top_of_ne, IsTree.dist_eq_dist_add_one_of_adj, IsAcyclic.dist_eq_dist_add_one_of_adj_of_reachable, dist_self, dist_eq_one_iff_adj, Connected.exists_path_of_dist, dist_bot, dist_le, Connected.diff_dist_adj, Reachable.dist_eq_zero_iff, Reachable.dist_triangle_right, dist_eq_zero_of_not_reachable, Reachable.exists_walk_length_eq_dist, exists_dist_eq_diam, dist_eq_zero_iff_eq_or_not_reachable, Connected.dist_eq_zero_iff, Reachable.pos_dist_of_ne, Adj.diff_dist_adj, Reachable.dist_triangle_left, Reachable.coe_dist_eq_edist, exists_walk_of_dist_ne_zero, Connected.pos_dist_of_ne, Reachable.exists_path_of_dist, dist_top
edist 📖CompOp
35 mathmath: ediam_le_iff, exists_edist_eq_ediam_of_ne_top, Walk.edist_le, ediam_eq_top, edist_eq_top_of_not_reachable, edist_self, edist_top, exists_edist_eq_radius_of_finite, edist_pos_of_ne, exists_edist_eq_eccent_of_finite, edist_le_eccent, edist_triangle, edist_bot, edist_eq_sInf, ediam_eq_iSup_iSup_edist, Connected.exists_walk_length_eq_edist, edist_anti, diam_def, edist_le_ediam, eccent_le_iff, ediam_def, exists_walk_of_edist_ne_top, Reachable.coe_dist_eq_edist, edist_comm, edist_eq_zero_iff, edist_le, Reachable.exists_walk_length_eq_edist, edist_top_of_ne, edist_boxProd, edist_eq_one_iff_adj, eccent_def, edist_bot_of_ne, exists_edist_eq_ediam_of_finite, edist_le_one_iff_adj_or_eq, radius_eq_iInf_iSup_edist

Theorems

NameKindAssumesProvesValidatesDepends On
dist_bot 📖mathematicaldist
Bot.bot
SimpleGraph
BooleanAlgebra.toBot
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
dist_self
dist_comm 📖mathematicaldistdist.eq_1
edist_comm
dist_eq_one_iff_adj 📖mathematicaldist
Adj
dist.eq_1
ENat.toNat_eq_iff
ENat.coe_one
edist_eq_one_iff_adj
dist_eq_sInf 📖mathematicaldist
InfSet.sInf
Nat.instInfSet
Set.range
Walk
Walk.length
ENat.iInf_toNat
dist_eq_zero_iff_eq_or_not_reachable 📖mathematicaldist
Reachable
dist_eq_sInf
dist_eq_zero_of_not_reachable 📖mathematicalReachabledist
dist_le 📖mathematicaldist
Walk.length
Nat.sInf_le
dist_eq_sInf
dist_ne_zero_iff_ne_and_reachable 📖mathematicalReachable
dist_self 📖mathematicaldist
dist_top 📖mathematicaldist
Top.top
SimpleGraph
BooleanAlgebra.toTop
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
dist_self
dist_top_of_ne 📖mathematicaldist
Top.top
SimpleGraph
BooleanAlgebra.toTop
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
edist_anti 📖mathematicalSimpleGraph
instLE
ENat
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
edist
Reachable.exists_walk_length_eq_edist
Walk.length_map
edist_le
le_top
edist_eq_top_of_not_reachable
edist_bot 📖mathematicaledist
Bot.bot
SimpleGraph
BooleanAlgebra.toBot
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
ENat
instZeroENat
Top.top
instTopENat
edist_self
edist_bot_of_ne
edist_bot_of_ne 📖mathematicaledist
Bot.bot
SimpleGraph
BooleanAlgebra.toBot
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
Top.top
ENat
instTopENat
Iff.not
edist_ne_top_iff_reachable
reachable_bot
edist_comm 📖mathematicaledistedist_eq_sInf
Set.image_univ
Set.image_univ_of_surjective
Walk.reverse_surjective
Set.image_comp
Walk.length_reverse
edist_eq_one_iff_adj 📖mathematicaledist
ENat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
Adj
exists_walk_of_edist_ne_top
Walk.adj_of_length_eq_one
Nat.cast_eq_one
le_antisymm
edist_le
Order.one_le_iff_pos
IsOrderedRing.toZeroLEOneClass
NeZero.one
edist_pos_of_ne
Adj.ne
edist_eq_sInf 📖mathematicaledist
InfSet.sInf
ENat
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
Set.range
Walk
ENat.instNatCast
Walk.length
edist_eq_top_of_not_reachable 📖mathematicalReachableedist
Top.top
ENat
instTopENat
ENat.iInf_eq_top_of_isEmpty
not_reachable_iff_isEmpty_walk
edist_eq_zero_iff 📖mathematicaledist
ENat
instZeroENat
edist_le 📖mathematicalENat
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
edist
ENat.instNatCast
Walk.length
sInf_le
edist_le_one_iff_adj_or_eq 📖mathematicalENat
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
edist
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
Adj
edist_self
edist_pos_of_ne
LE.le.ge_iff_eq'
Order.one_le_iff_pos
IsOrderedRing.toZeroLEOneClass
NeZero.one
edist_eq_one_iff_adj
edist_ne_top_iff_reachable 📖mathematicalReachablereachable_of_edist_ne_top
Reachable.elim
edist_pos_of_ne 📖mathematicalENat
Preorder.toLT
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
instZeroENat
edist
pos_iff_ne_zero
Iff.ne
edist_eq_zero_iff
edist_self 📖mathematicaledist
ENat
instZeroENat
edist_eq_zero_iff
edist_top 📖mathematicaledist
Top.top
SimpleGraph
BooleanAlgebra.toTop
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
ENat
instZeroENat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
edist_self
edist_top_of_ne 📖mathematicaledist
Top.top
SimpleGraph
BooleanAlgebra.toTop
CompleteBooleanAlgebra.toBooleanAlgebra
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
completeAtomicBooleanAlgebra
ENat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
edist_triangle 📖mathematicalENat
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
edist
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
eq_or_ne
top_add
add_top
exists_walk_of_edist_ne_top
Nat.cast_add
Walk.length_append
edist_le
exists_walk_of_dist_ne_zero 📖mathematicalWalk.length
dist
Reachable.exists_walk_length_eq_dist
Reachable.of_dist_ne_zero
exists_walk_of_edist_eq_coe 📖mathematicaledist
ENat
ENat.instNatCast
Walk.lengthENat.coe_ne_top
exists_walk_of_edist_ne_top
Nat.cast_injective
exists_walk_of_edist_ne_top 📖mathematicalENat
ENat.instNatCast
Walk.length
edist
Reachable.exists_walk_length_eq_edist
reachable_of_edist_ne_top
length_eq_dist_of_subwalk 📖Walk.length
dist
Walk.IsSubwalk
LE.le.eq_of_not_lt'
dist_le
Reachable.exists_path_of_dist
Walk.reachable
Walk.length_append
nonempty_of_pos_dist 📖mathematicaldistSet.Nonempty
Walk
Set.univ
Nat.nonempty_of_pos_sInf
dist_eq_sInf
reachable_of_edist_ne_top 📖mathematicalReachableFunction.mt
edist_eq_top_of_not_reachable

SimpleGraph.Adj

Theorems

NameKindAssumesProvesValidatesDepends On
diff_dist_adj 📖mathematicalSimpleGraph.AdjSimpleGraph.distSimpleGraph.dist_eq_one_iff_adj
symm
SimpleGraph.Reachable.dist_triangle_right
reachable
SimpleGraph.Reachable.dist_triangle_left

SimpleGraph.Connected

Theorems

NameKindAssumesProvesValidatesDepends On
diff_dist_adj 📖mathematicalSimpleGraph.Connected
SimpleGraph.Adj
SimpleGraph.distSimpleGraph.Adj.diff_dist_adj
dist_eq_zero_iff 📖mathematicalSimpleGraph.ConnectedSimpleGraph.distpreconnected
dist_triangle 📖mathematicalSimpleGraph.ConnectedSimpleGraph.distexists_walk_length_eq_dist
SimpleGraph.Walk.length_append
SimpleGraph.dist_le
exists_path_of_dist 📖mathematicalSimpleGraph.ConnectedSimpleGraph.Walk.IsPath
SimpleGraph.Walk.length
SimpleGraph.dist
exists_walk_length_eq_dist
SimpleGraph.Walk.isPath_of_length_eq_dist
exists_walk_length_eq_dist 📖mathematicalSimpleGraph.ConnectedSimpleGraph.Walk.length
SimpleGraph.dist
SimpleGraph.Reachable.exists_walk_length_eq_dist
preconnected
SimpleGraph.dist_eq_sInf
exists_walk_length_eq_edist 📖mathematicalSimpleGraph.ConnectedENat
ENat.instNatCast
SimpleGraph.Walk.length
SimpleGraph.edist
SimpleGraph.Reachable.exists_walk_length_eq_edist
preconnected
one_lt_dist_of_ne_of_not_adj 📖mathematicalSimpleGraph.Connected
SimpleGraph.Adj
SimpleGraph.distSimpleGraph.Reachable.one_lt_dist_of_ne_of_not_adj
preconnected
pos_dist_of_ne 📖mathematicalSimpleGraph.ConnectedSimpleGraph.distdist_eq_zero_iff

SimpleGraph.Reachable

Theorems

NameKindAssumesProvesValidatesDepends On
coe_dist_eq_edist 📖mathematicalENat
ENat.instNatCast
SimpleGraph.dist
SimpleGraph.edist
ENat.coe_toNat
SimpleGraph.edist_ne_top_iff_reachable
dist_anti 📖mathematicalSimpleGraph
SimpleGraph.instLE
SimpleGraph.distexists_walk_length_eq_dist
SimpleGraph.Walk.length_map
SimpleGraph.dist_le
dist_eq_zero_iff 📖mathematicalSimpleGraph.dist
dist_triangle_left 📖mathematicalSimpleGraph.distENat.coe_le_coe
ENat.coe_add
dist_triangle_right 📖mathematicalSimpleGraph.distENat.coe_le_coe
ENat.coe_add
exists_path_of_dist 📖mathematicalSimpleGraph.Walk.IsPath
SimpleGraph.Walk.length
SimpleGraph.dist
exists_walk_length_eq_dist
SimpleGraph.Walk.isPath_of_length_eq_dist
exists_walk_length_eq_dist 📖mathematicalSimpleGraph.Walk.length
SimpleGraph.dist
Nat.sInf_mem
Set.range_nonempty_iff_nonempty
SimpleGraph.dist_eq_sInf
exists_walk_length_eq_edist 📖mathematicalENat
ENat.instNatCast
SimpleGraph.Walk.length
SimpleGraph.edist
csInf_mem
Set.range_nonempty_iff_nonempty
of_dist_ne_zero 📖mathematicalSimpleGraph.ReachableSimpleGraph.dist_ne_zero_iff_ne_and_reachable
one_lt_dist_of_ne_of_not_adj 📖mathematicalSimpleGraph.AdjSimpleGraph.distpos_dist_of_ne
exists_walk_length_eq_dist
SimpleGraph.Walk.exists_length_eq_one_iff
pos_dist_of_ne 📖mathematicalSimpleGraph.dist

SimpleGraph.Walk

Theorems

NameKindAssumesProvesValidatesDepends On
edist_le 📖mathematicalENat
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrderENat
SimpleGraph.edist
ENat.instNatCast
length
SimpleGraph.edist_le
exists_adj_adj_not_adj_ne 📖mathematicallength
SimpleGraph.dist
SimpleGraph.Adjlength_tail_add_one
getVert_tail
SimpleGraph.dist_le
adj_snd
adj_getVert_succ
isPath_of_length_eq_dist 📖mathematicallength
SimpleGraph.dist
IsPathbypass_eq_self_of_length_le
SimpleGraph.dist_le
bypass_isPath

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