Documentation Verification Report

Invariants

📁 Source: Mathlib/Data/Ordmap/Invariants.lean

Statistics

MetricCount
Definitionsdec, BalancedSz, dec, Raised, Sized, balance', balanceL', balanceR', node3L, node3R, node4L, node4R, realSize, rotateL, rotateR
15
Theoremsimp, imp, dual, dual, dual_iff, mem_gt, mem_lt, mono_left, mono_right, of_gt, of_lt, to_lt, to_nil, to_sep, trans_left, trans_right, weak, weak_left, weak_right, add_left, add_right, dist_le, dist_le', right, balance', dual, dual_iff, eq_node', induction, node', node3L, node3R, node4L, pos, rotateL, rotateL_size, rotateR, rotateR_size, size_eq, size_eq_zero, all_balance', all_balanceL, all_balanceR, all_dual, all_iff_forall, all_node', all_node3L, all_node3R, all_node4L, all_node4R, all_rotateL, all_rotateR, all_singleton, any_iff_exists, any_singleton, balanceL_eq_balance, balanceL_eq_balance', balanceR_eq_balance', balance_eq_balance', balance_sz_dual, balancedSz_down, balancedSz_up, balancedSz_zero, delta_lt_false, dual_balance', dual_balanceL, dual_balanceR, dual_dual, dual_eraseMax, dual_eraseMin, dual_insert, dual_node', dual_node3L, dual_node3R, dual_node4L, dual_node4R, dual_rotateL, dual_rotateR, emem_iff_all, emem_iff_mem_toList, equiv_iff, findMax'_all, findMax'_dual, findMax_dual, findMin'_all, findMin'_dual, findMin_dual, foldr_cons_eq_toList, length_toList, length_toList', merge_nil_left, merge_nil_right, merge_node, node3L_size, node3R_size, node4L_size, not_le_delta, pos_size_of_mem, raised_iff, rotateL_nil, rotateL_node, rotateR_nil, rotateR_node, size_balance', size_balanceL, size_balanceR, size_dual, size_eq_realSize, splitMax_eq, splitMin_eq, toList_nil, toList_node
112
Total127

Ordnode

Definitions

NameCategoryTheorems
BalancedSz 📖MathDef
1 mathmath: balancedSz_zero
Raised 📖MathDef
3 mathmath: raised_iff, insertWith.valid_aux, Valid'.erase_aux
Sized 📖MathDef
2 mathmath: Sized.dual_iff, Valid'.sz
balance' 📖CompOp
9 mathmath: balanceL_eq_balance', balance_eq_balance', Valid'.balance', balanceR_eq_balance', size_balance', all_balance', Valid'.balance'_aux, dual_balance', Sized.balance'
balanceL' 📖CompOp
balanceR' 📖CompOp
node3L 📖CompOp
7 mathmath: dual_node3L, Valid'.node3L, Sized.node3L, rotateL_node, dual_node3R, node3L_size, all_node3L
node3R 📖CompOp
7 mathmath: node3R_size, Sized.node3R, all_node3R, Valid'.node3R, dual_node3L, dual_node3R, rotateR_node
node4L 📖CompOp
7 mathmath: node4L_size, dual_node4L, all_node4L, dual_node4R, rotateL_node, Valid'.node4L, Sized.node4L
node4R 📖CompOp
4 mathmath: all_node4R, dual_node4L, dual_node4R, rotateR_node
realSize 📖CompOp
2 mathmath: size_eq_realSize, length_toList'
rotateL 📖CompOp
8 mathmath: Sized.rotateL_size, dual_rotateR, all_rotateL, dual_rotateL, Valid'.rotateL, rotateL_node, Sized.rotateL, rotateL_nil
rotateR 📖CompOp
8 mathmath: dual_rotateR, Sized.rotateR_size, rotateR_nil, dual_rotateL, Sized.rotateR, rotateR_node, all_rotateR, Valid'.rotateR

Theorems

NameKindAssumesProvesValidatesDepends On
all_balance' 📖mathematicalAll
balance'
balance'.eq_1
all_balanceL 📖mathematicalBalanced
Sized
Raised
size
BalancedSz
All
balanceL
balanceL_eq_balance'
all_balance'
all_balanceR 📖mathematicalBalanced
Sized
Raised
size
BalancedSz
All
balanceR
balanceR_eq_balance'
all_balance'
all_dual 📖mathematicalAll
dual
all_iff_forall 📖mathematicalAll
all_node' 📖mathematicalAll
node'
all_node3L 📖mathematicalAll
node3L
all_node3R 📖mathematicalAll
node3R
all_node4L 📖mathematicalAll
node4L
all_node4R 📖mathematicalAll
node4R
all_rotateL 📖mathematicalAll
rotateL
all_rotateR 📖mathematicalAll
rotateR
all_dual
dual_rotateR
all_rotateL
all_singleton 📖mathematicalAll
Ordnode
instSingleton
any_iff_exists 📖mathematicalAny
Emem
any_singleton 📖mathematicalAny
Ordnode
instSingleton
balanceL_eq_balance 📖mathematicalSized
size
delta
balanceL
balance
add_eq_zero
Unique.instSubsingleton
Nat.instCanonicallyOrderedAdd
size.eq_2
Sized.size_eq_zero
Sized.eq_node'
not_lt_of_ge
Sized.pos
add_comm
balanceL_eq_balance' 📖mathematicalBalanced
Sized
Raised
size
BalancedSz
balanceL
balance'
balance_eq_balance'
balanceL_eq_balance
balancedSz_zero
BalancedSz.symm
le_trans
raised_iff
mul_pos
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
balanceR_eq_balance' 📖mathematicalBalanced
Sized
Raised
size
BalancedSz
balanceR
balance'
dual_dual
dual_balanceR
balanceL_eq_balance'
Balanced.dual
Sized.dual
balance_sz_dual
dual_balance'
balance_eq_balance' 📖mathematicalBalanced
Sized
balance
balance'
Sized.eq_node'
balancedSz_zero
BalancedSz.symm
add_eq_zero
Unique.instSubsingleton
Nat.instCanonicallyOrderedAdd
size.eq_2
Sized.size_eq_zero
rotateL_node
zero_add
not_le_of_gt
add_pos
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
Sized.pos
rotateL.eq_1
Mathlib.Tactic.Abel.subst_into_add
Mathlib.Tactic.Abel.term_atom
Mathlib.Tactic.Abel.term_add_const
Mathlib.Tactic.Abel.const_add_term
add_zero
Mathlib.Tactic.Abel.term_add_term
Mathlib.Meta.NormNum.IsNat.to_eq
Mathlib.Meta.NormNum.isNat_add
Mathlib.Meta.NormNum.isNat_ofNat
rotateR_node
rotateR.eq_1
add_le_add
covariant_swap_add_of_covariant_add
lt_of_le_of_lt
le_trans
size.eq_1
balance_sz_dual 📖mathematicalRaised
size
BalancedSz
dualsize_dual
BalancedSz.symm
balancedSz_down 📖delta
BalancedSz
le_trans
balancedSz_up 📖delta
BalancedSz
le_trans
balancedSz_zero 📖mathematicalBalancedSzadd_zero
MulZeroClass.mul_zero
Nat.instCanonicallyOrderedAdd
delta_lt_false 📖deltanot_le_of_gt
lt_trans
mul_lt_mul_of_pos_left
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
one_mul
mul_assoc
dual_balance' 📖mathematicaldual
balance'
size_dual
add_comm
dual_rotateL
delta_lt_false
dual_rotateR
dual_balanceL 📖mathematicaldual
balanceL
balanceR
add_comm
size_dual
dual_balanceR 📖mathematicaldual
balanceR
balanceL
dual_dual
dual_balanceL
dual_dual 📖mathematicaldualdual.eq_2
dual_eraseMax 📖mathematicaldual
eraseMax
eraseMin
dual_dual
dual_eraseMin
dual_eraseMin 📖mathematicaldual
eraseMin
eraseMax
eraseMin.eq_3
dual_balanceR
dual.eq_2
eraseMax.eq_3
dual_insert 📖mathematicaldual
insert
OrderDual
OrderDual.instLE
insert.eq_2
dual.eq_2
cmpLE_swap
dual_balanceL
dual_balanceR
dual_node' 📖mathematicaldual
node'
add_comm
size_dual
dual_node3L 📖mathematicaldual
node3L
node3R
add_comm
size_dual
dual_node3R 📖mathematicaldual
node3R
node3L
add_comm
size_dual
dual_node4L 📖mathematicaldual
node4L
node4R
dual_node3L
add_comm
size_dual
dual_node4R 📖mathematicaldual
node4R
node4L
dual_node3R
add_comm
size_dual
dual_rotateL 📖mathematicaldual
rotateL
rotateR
add_zero
size_dual
zero_add
dual_node3L
dual_node4L
dual_rotateR 📖mathematicaldual
rotateR
rotateL
dual_dual
dual_rotateL
emem_iff_all 📖mathematicalEmemall_iff_forall
emem_iff_mem_toList 📖mathematicalEmem
toList
toList_node
equiv_iff 📖mathematicalSizedEquiv
toList
length_toList
findMax'_all 📖mathematicalAllfindMax'
findMax'_dual 📖mathematicalfindMax'
dual
findMin'
findMin'_dual
dual_dual
findMax_dual 📖mathematicalfindMax
dual
findMin
findMin_dual
dual_dual
findMin'_all 📖mathematicalAllfindMin'
findMin'_dual 📖mathematicalfindMin'
dual
findMax'
findMin_dual 📖mathematicalfindMin
dual
findMax
findMin'_dual
foldr_cons_eq_toList 📖mathematicalfoldr
toList
foldr.eq_2
length_toList 📖mathematicalSizedtoList
size
length_toList'
size_eq_realSize
length_toList' 📖mathematicaltoList
realSize
toList_node
merge_nil_left 📖mathematicalmerge
nil
merge_nil_right 📖mathematicalmerge
nil
merge_node 📖mathematicalmerge
node
Ordnode
delta
balanceL
balanceR
glue
node3L_size 📖mathematicalsize
node3L
add_right_comm
node3R_size 📖mathematicalsize
node3R
add_assoc
node4L_size 📖mathematicalSizedsize
node4L
add_zero
Mathlib.Tactic.Abel.subst_into_add
Mathlib.Tactic.Abel.term_atom
Mathlib.Tactic.Abel.term_add_const
zero_add
Mathlib.Tactic.Abel.const_add_term
Mathlib.Tactic.Abel.term_add_term
Mathlib.Meta.NormNum.IsNat.to_eq
Mathlib.Meta.NormNum.isNat_add
Mathlib.Meta.NormNum.isNat_ofNat
not_le_delta 📖mathematicaldeltanot_le_of_gt
pos_size_of_mem 📖mathematicalSized
Ordnode
instMembership
sizeIsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
contravariant_swap_add_of_contravariant_add
contravariant_lt_of_covariant_le
Nat.instCanonicallyOrderedAdd
Nat.instZeroLEOneClass
raised_iff 📖mathematicalRaisedle_rfl
eq_or_lt_of_le
le_antisymm
rotateL_nil 📖mathematicalrotateL
nil
node'
rotateL_node 📖mathematicalrotateL
node
Ordnode
size
ratio
node3L
node4L
rotateR_nil 📖mathematicalrotateR
nil
node'
rotateR_node 📖mathematicalrotateR
node
Ordnode
size
ratio
node3R
node4R
size_balance' 📖mathematicalSizedsize
balance'
Sized.rotateL_size
Sized.rotateR_size
size_balanceL 📖mathematicalBalanced
Sized
Raised
size
BalancedSz
balanceLbalanceL_eq_balance'
size_balance'
size_balanceR 📖mathematicalBalanced
Sized
Raised
size
BalancedSz
balanceRbalanceR_eq_balance'
size_balance'
size_dual 📖mathematicalsize
dual
size_eq_realSize 📖mathematicalSizedsize
realSize
size.eq_2
splitMax_eq 📖mathematicalsplitMax'
Ordnode
eraseMax
node
findMax'
splitMax'.eq_2
findMax'.eq_2
eraseMax.eq_3
splitMin_eq 📖mathematicalsplitMin'
Ordnode
findMin'
eraseMin
node
splitMin'.eq_2
findMin'.eq_2
eraseMin.eq_3
toList_nil 📖mathematicaltoList
nil
toList_node 📖mathematicaltoList
node
toList.eq_1
foldr.eq_2
foldr_cons_eq_toList

Ordnode.All

Theorems

NameKindAssumesProvesValidatesDepends On
imp 📖Ordnode.All

Ordnode.Any

Theorems

NameKindAssumesProvesValidatesDepends On
imp 📖Ordnode.Any

Ordnode.Balanced

Definitions

NameCategoryTheorems
dec 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
dual 📖mathematicalOrdnode.BalancedOrdnode.dualOrdnode.size_dual
Ordnode.BalancedSz.symm

Ordnode.BalancedSz

Definitions

NameCategoryTheorems
dec 📖CompOp

Ordnode.Bounded

Theorems

NameKindAssumesProvesValidatesDepends On
dual 📖mathematicalOrdnode.BoundedOrderDual
OrderDual.instPreorder
Ordnode.dual
dual_iff 📖mathematicalOrdnode.Bounded
OrderDual
OrderDual.instPreorder
Ordnode.dual
dual
OrderDual.Preorder.dual_dual
Ordnode.dual_dual
mem_gt 📖mathematicalOrdnode.Bounded
WithBot.some
Ordnode.All
Preorder.toLT
to_lt
Ordnode.All.imp
lt_trans
mem_lt 📖mathematicalOrdnode.Bounded
WithTop.some
Ordnode.All
Preorder.toLT
Ordnode.All.imp
lt_trans
to_lt
mono_left 📖Preorder.toLE
Ordnode.Bounded
WithBot.some
lt_of_le_of_lt
mono_right 📖Preorder.toLE
Ordnode.Bounded
WithTop.some
lt_of_lt_of_le
of_gt 📖Ordnode.Bounded
Ordnode.nil
WithBot.some
Ordnode.All
Preorder.toLT
of_lt 📖Ordnode.Bounded
Ordnode.nil
WithTop.some
Ordnode.All
Preorder.toLT
to_lt 📖mathematicalOrdnode.Bounded
WithBot.some
WithTop.some
Preorder.toLTlt_trans
to_nil 📖mathematicalOrdnode.BoundedOrdnode.nilto_lt
to_sep 📖mathematicalOrdnode.Bounded
WithTop.some
WithBot.some
Ordnode.All
Preorder.toLT
Ordnode.All.imp
lt_trans
mem_gt
mem_lt
trans_left 📖Ordnode.Bounded
WithTop.some
WithBot.some
weak_left
mono_left
le_of_lt
to_lt
trans_right 📖Ordnode.Bounded
WithTop.some
WithBot.some
weak_right
mono_right
le_of_lt
to_lt
weak 📖mathematicalOrdnode.BoundedBot.bot
WithBot
WithBot.bot
Top.top
WithTop
WithTop.top
weak_right
weak_left
weak_left 📖mathematicalOrdnode.BoundedBot.bot
WithBot
WithBot.bot
weak_right 📖mathematicalOrdnode.BoundedTop.top
WithTop
WithTop.top

Ordnode.Raised

Theorems

NameKindAssumesProvesValidatesDepends On
add_left 📖Ordnode.Raised
add_right 📖Ordnode.Raisedadd_comm
add_left
dist_le 📖mathematicalOrdnode.RaisedNat.distOrdnode.raised_iff
Nat.dist_eq_sub_of_le
tsub_le_iff_left
Nat.instOrderedSub
dist_le' 📖mathematicalOrdnode.RaisedNat.distNat.dist_comm
dist_le
right 📖mathematicalOrdnode.Raised
Ordnode.size
Ordnode.node'Ordnode.node'.eq_1
Ordnode.size_node

Ordnode.Sized

Theorems

NameKindAssumesProvesValidatesDepends On
balance' 📖mathematicalOrdnode.SizedOrdnode.balance'node'
rotateL
rotateR
dual 📖mathematicalOrdnode.SizedOrdnode.dualadd_comm
Ordnode.size_dual
dual_iff 📖mathematicalOrdnode.Sized
Ordnode.dual
Ordnode.dual_dual
dual
eq_node' 📖mathematicalOrdnode.Sized
Ordnode.node
Ordnode.node'
induction 📖Ordnode.Sized
Ordnode.nil
Ordnode.node'
eq_node'
node' 📖mathematicalOrdnode.SizedOrdnode.node'
node3L 📖mathematicalOrdnode.SizedOrdnode.node3Lnode'
node3R 📖mathematicalOrdnode.SizedOrdnode.node3Rnode'
node4L 📖mathematicalOrdnode.SizedOrdnode.node4Lnode'
pos 📖Ordnode.Sized
Ordnode.node
rotateL 📖mathematicalOrdnode.SizedOrdnode.rotateLnode'
Ordnode.rotateL_node
node3L
node4L
rotateL_size 📖mathematicalOrdnode.SizedOrdnode.size
Ordnode.rotateL
add_zero
Ordnode.node3L_size
Mathlib.Tactic.Abel.subst_into_add
Mathlib.Tactic.Abel.term_atom
Mathlib.Tactic.Abel.term_add_const
zero_add
Ordnode.node4L_size
rotateR 📖mathematicalOrdnode.SizedOrdnode.rotateRdual_iff
Ordnode.dual_rotateR
rotateL
dual
rotateR_size 📖mathematicalOrdnode.SizedOrdnode.size
Ordnode.rotateR
Ordnode.size_dual
Ordnode.dual_rotateR
rotateL_size
dual
add_comm
size_eq 📖mathematicalOrdnode.Sized
Ordnode.node
Ordnode.size
size_eq_zero 📖mathematicalOrdnode.SizedOrdnode.size
Ordnode.nil

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