Datasets:
CloKTech
/
MesoMathematics

Dataset card Data Studio Files
xet
 Community
1
definition_height
int64
0
59
⌀
is_auto_or_private
bool
2 classes
is_internal_name
bool
2 classes
kind
stringclasses
7 values
module
stringlengths
12
90
name
stringlengths
2
347
namespace
stringlengths
0
235
reducibility
stringclasses
3 values
statement_dag_size
int64
1
13.9k
type_refs
listlengths
0
229
value_dag_size
int64
1
95.1k
⌀
value_refs
listlengths
0
699
1
true
false
definition
Mathlib.Data.List.AList
AList.ctorIdx
AList
regular
12
[ "AList", "Nat" ]
12
[ "AList" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.empty_entries
AList
null
31
[ "AList", "AList.entries", "AList.instEmptyCollection", "EmptyCollection.emptyCollection", "Eq", "List", "List.nil", "Sigma" ]
28
[ "AList", "AList.entries", "AList.instEmptyCollection", "EmptyCollection.emptyCollection", "List", "Sigma", "rfl" ]
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.empty_lookupFinsupp
AList
null
45
[ "AList", "AList.instEmptyCollection", "AList.lookupFinsupp", "EmptyCollection.emptyCollection", "Eq", "Finsupp", "Finsupp.instZero", "OfNat.ofNat", "Zero", "Zero.toOfNat0" ]
32
[ "AList", "AList.instEmptyCollection", "AList.lookupFinsupp", "EmptyCollection.emptyCollection", "Finsupp", "Zero", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.empty_union
AList
null
37
[ "AList", "AList.instEmptyCollection", "AList.instUnion", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Union.union" ]
51
[ "AList", "AList.entries", "AList.ext", "AList.instEmptyCollection", "AList.instUnion", "DecidableEq", "EmptyCollection.emptyCollection", "List", "Sigma", "Union.union", "rfl" ]
null
false
false
abbrev
Mathlib.Data.List.AList
AList.entries
AList
abbrev
17
[ "AList", "List", "Sigma" ]
12
[ "AList" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.entries_insert
AList
null
57
[ "AList", "AList.entries", "AList.insert", "DecidableEq", "Eq", "List", "List.cons", "List.kerase", "Sigma", "Sigma.mk" ]
40
[ "AList", "AList.entries", "AList.insert", "DecidableEq", "List", "Sigma", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.entries_insert_of_notMem
AList
null
66
[ "AList", "AList.entries", "AList.insert", "AList.instMembership", "DecidableEq", "Eq", "List", "List.cons", "Membership.mem", "Not", "Sigma", "Sigma.mk" ]
154
[ "AList", "AList.entries", "AList.entries_insert", "AList.insert", "AList.instMembership", "DecidableEq", "Eq", "Eq.mpr", "Eq.refl", "List", "List.cons", "List.kerase", "List.kerase_of_notMem_keys", "Membership.mem", "Not", "Sigma", "Sigma.mk", "congrArg", "id" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.entries_toAList
AList
null
39
[ "AList.entries", "DecidableEq", "Eq", "List", "List.dedupKeys", "List.toAList", "Sigma" ]
33
[ "AList.entries", "DecidableEq", "List", "List.toAList", "Sigma", "rfl" ]
4
false
false
definition
Mathlib.Data.List.AList
AList.erase
AList
regular
20
[ "AList", "DecidableEq" ]
39
[ "AList", "AList.entries", "AList.erase._proof_1", "AList.mk", "DecidableEq", "List.kerase" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.erase._proof_1
AList.erase
null
32
[ "AList", "AList.entries", "DecidableEq", "List.NodupKeys", "List.kerase" ]
33
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.NodupKeys.kerase" ]
null
true
false
theorem
Mathlib.Data.Finmap
AList.erase.eq_1
AList.erase
null
51
[ "AList", "AList.entries", "AList.erase", "AList.erase._proof_1", "AList.mk", "DecidableEq", "Eq", "List.kerase" ]
29
[ "AList", "AList.erase", "DecidableEq", "Eq.refl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.erase_erase
AList
null
36
[ "AList", "AList.erase", "DecidableEq", "Eq" ]
47
[ "AList", "AList.entries", "AList.erase", "AList.ext", "DecidableEq", "List.kerase_kerase" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.ext
AList
null
37
[ "AList", "AList.entries", "Eq", "List", "Sigma" ]
174
[ "AList", "AList.entries", "AList.mk", "Eq", "Eq.ndrec", "Eq.rec", "Eq.refl", "List", "List.NodupKeys", "Sigma", "_private.Mathlib.Data.List.AList.0.AList.ext.match_1_1" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.ext_iff
AList
null
38
[ "AList", "AList.entries", "Eq", "Iff", "List", "Sigma" ]
161
[ "AList", "AList.entries", "AList.ext", "Eq", "Eq.casesOn", "Eq.ndrec", "Eq.refl", "Eq.symm", "HEq", "HEq.refl", "Iff.intro", "List", "Sigma" ]
5
false
false
definition
Mathlib.Data.List.AList
AList.extract
AList
regular
26
[ "AList", "DecidableEq", "Option", "Prod" ]
128
[ "AList", "AList.entries", "AList.extract._proof_3", "AList.extract.match_1", "AList.mk", "DecidableEq", "List", "List.NodupKeys", "List.kextract", "Option", "Prod", "Prod.mk", "Prod.snd", "Sigma" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.extract._proof_3
AList.extract
null
44
[ "AList", "AList.entries", "DecidableEq", "List", "List.NodupKeys", "List.kextract", "Option", "Prod.snd", "Sigma" ]
116
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "Eq", "Eq.mpr", "List", "List.NodupKeys", "List.NodupKeys.kerase", "List.dlookup", "List.kerase", "List.kextract", "List.kextract_eq_dlookup_kerase", "Option", "Prod", "Prod.mk", "Prod.snd", "Sigma", "congrArg", "id" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.extract.eq_1
AList.extract
null
120
[ "AList", "AList.entries", "AList.extract", "AList.extract._proof_3", "AList.extract.match_1", "AList.mk", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.kextract", "Option", "Prod", "Prod.mk", "Prod.snd", "Sigma" ]
35
[ "AList", "AList.extract", "DecidableEq", "Eq.refl", "Option", "Prod" ]
null
true
false
abbrev
Mathlib.Data.List.AList
AList.extract.match_1
AList.extract
abbrev
95
[ "List", "List.NodupKeys", "Option", "Prod", "Prod.mk", "Prod.snd", "Sigma" ]
127
[ "List", "List.NodupKeys", "Option", "Prod", "Prod.casesOn", "Prod.mk", "Prod.snd", "Sigma" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.extract_eq_lookup_erase
AList
null
53
[ "AList", "AList.erase", "AList.extract", "AList.lookup", "DecidableEq", "Eq", "Option", "Prod", "Prod.mk" ]
243
[ "AList", "AList.entries", "AList.erase", "AList.extract", "AList.extract._proof_3", "AList.lookup", "AList.mk", "AList.mk.congr_simp", "And", "And.intro", "DecidableEq", "Eq", "Eq.mpr", "Eq.ndrec", "Eq.refl", "Eq.trans", "List", "List.NodupKeys", "List.dlookup", "List.kerase", ...
2
false
false
definition
Mathlib.Data.List.AList
AList.foldl
AList
regular
21
[ "AList" ]
52
[ "AList", "AList.entries", "List.foldl", "Sigma", "Sigma.fst", "Sigma.snd" ]
5
false
false
definition
Mathlib.Data.List.AList
AList.insert
AList
regular
23
[ "AList", "DecidableEq" ]
44
[ "AList", "AList.entries", "AList.insert._proof_1", "AList.mk", "DecidableEq", "List.kinsert" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insert._proof_1
AList.insert
null
36
[ "AList", "AList.entries", "DecidableEq", "List.NodupKeys", "List.kinsert" ]
37
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.kinsert_nodupKeys" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.insert.eq_1
AList.insert
null
57
[ "AList", "AList.entries", "AList.insert", "AList.insert._proof_1", "AList.mk", "DecidableEq", "Eq", "List.kinsert" ]
33
[ "AList", "AList.insert", "DecidableEq", "Eq.refl" ]
6
false
false
definition
Mathlib.Data.List.AList
AList.insertRec
AList
regular
69
[ "AList", "AList.insert", "AList.instEmptyCollection", "AList.instMembership", "DecidableEq", "EmptyCollection.emptyCollection", "Membership.mem", "Not" ]
286
[ "AList", "AList._sizeOf_inst", "AList.insert", "AList.insertRec._proof_1", "AList.insertRec._proof_2", "AList.insertRec._proof_3", "AList.insertRec._proof_4", "AList.insertRec.match_1", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyColl...
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_1
AList.insertRec
null
34
[ "AList", "AList._sizeOf_inst", "WellFounded", "instSizeOfDefault", "invImage", "sizeOfWFRel" ]
38
[ "AList", "AList._sizeOf_inst", "Lean.opaqueId", "WellFounded", "instSizeOfDefault", "invImage", "sizeOfWFRel" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_2
AList.insertRec
null
80
[ "AList", "AList.insert", "AList.mk", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd" ]
101
[ "AList", "AList.insert", "AList.mk", "AList.mk_cons_eq_insert", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd", "congrArg", "id" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_3
AList.insertRec
null
65
[ "AList.entries", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.instMembership", "List.keys", "List.nodupKeys_of_nodupKeys_cons", "Membership.mem", "Not", "Sigma", "Sigma.fst" ]
51
[ "AList.entries", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "List.notMem_keys_of_nodupKeys_cons", "Sigma" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_4
AList.insertRec
null
74
[ "AList", "AList._sizeOf_inst", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "instSizeOfDefault", "invImage", "sizeOfWFRel" ]
554
[ "AList", "AList._sizeOf_inst", "AList.mk", "AList.mk.sizeOf_spec", "Bool", "Bool.true", "Decidable.byContradiction", "Decidable.decide", "Eq", "Eq.mpr", "Eq.refl", "Eq.symm", "Eq.trans", "HAdd.hAdd", "HSub.hSub", "Int", "Int.instAdd", "Int.instLEInt", "Int.instNegInt", "Int.ins...
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_5
AList.insertRec
null
80
[ "AList", "AList.insert", "AList.mk", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd" ]
101
[ "AList", "AList.insert", "AList.mk", "AList.mk_cons_eq_insert", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd", "congrArg", "id" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_6
AList.insertRec
null
65
[ "AList.entries", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.instMembership", "List.keys", "List.nodupKeys_of_nodupKeys_cons", "Membership.mem", "Not", "Sigma", "Sigma.fst" ]
51
[ "AList.entries", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "List.notMem_keys_of_nodupKeys_cons", "Sigma" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_7
AList.insertRec
null
80
[ "AList", "AList.insert", "AList.mk", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd" ]
101
[ "AList", "AList.insert", "AList.mk", "AList.mk_cons_eq_insert", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd", "congrArg", "id" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.insertRec._proof_8
AList.insertRec
null
65
[ "AList.entries", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.instMembership", "List.keys", "List.nodupKeys_of_nodupKeys_cons", "Membership.mem", "Not", "Sigma", "Sigma.fst" ]
51
[ "AList.entries", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "List.notMem_keys_of_nodupKeys_cons", "Sigma" ]
null
true
true
definition
Mathlib.Data.List.AList
AList.insertRec._unsafe_rec
AList.insertRec
opaque
69
[ "AList", "AList.insert", "AList.instEmptyCollection", "AList.instMembership", "DecidableEq", "EmptyCollection.emptyCollection", "Membership.mem", "Not" ]
186
[ "AList", "AList.entries", "AList.insert", "AList.insertRec._unsafe_rec", "AList.insertRec.match_1", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "AList.mk_cons_eq_insert", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Eq.mpr", "List", "List.NodupKeys", "L...
null
true
false
theorem
Mathlib.Data.List.AList
AList.insertRec.eq_1
AList.insertRec
null
96
[ "AList", "AList.insert", "AList.insertRec", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "List.NodupKeys", "List.nil", "Membership.mem", "Not", "Sigma" ]
199
[ "AList", "AList.insert", "AList.insertRec", "AList.insertRec._proof_5", "AList.insertRec._proof_6", "AList.insertRec.eq_def", "AList.insertRec.match_1", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyCollection", "Eq.mpr", "Eq.refl", ...
null
true
false
theorem
Mathlib.Data.List.AList
AList.insertRec.eq_2
AList.insertRec
null
156
[ "AList", "AList.insert", "AList.insertRec", "AList.insertRec._proof_5", "AList.insertRec._proof_6", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Eq.mpr", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_...
261
[ "AList", "AList.insert", "AList.insertRec", "AList.insertRec._proof_5", "AList.insertRec._proof_6", "AList.insertRec.eq_def", "AList.insertRec.match_1", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyCollection", "Eq.mpr", "Eq.refl", ...
null
true
false
theorem
Mathlib.Data.List.AList
AList.insertRec.eq_def
AList.insertRec
null
177
[ "AList", "AList.insert", "AList.insertRec", "AList.insertRec._proof_5", "AList.insertRec._proof_6", "AList.insertRec.match_1", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Eq.mpr", "List", "List.NodupKeys", "L...
760
[ "AList", "AList._sizeOf_inst", "AList.entries", "AList.insert", "AList.insertRec", "AList.insertRec._proof_1", "AList.insertRec._proof_2", "AList.insertRec._proof_3", "AList.insertRec._proof_4", "AList.insertRec._proof_5", "AList.insertRec._proof_6", "AList.insertRec.match_1", "AList.instEmp...
null
true
false
abbrev
Mathlib.Data.List.AList
AList.insertRec.match_1
AList.insertRec
abbrev
70
[ "AList", "AList.mk", "List", "List.NodupKeys", "List.cons", "List.nil", "Sigma" ]
128
[ "AList", "AList.casesOn", "AList.mk", "List", "List.NodupKeys", "List.casesOn", "List.cons", "List.nil", "Sigma" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.insertRec_empty
AList
null
84
[ "AList", "AList.insert", "AList.insertRec", "AList.instEmptyCollection", "AList.instMembership", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Membership.mem", "Not" ]
151
[ "AList", "AList.insert", "AList.insertRec", "AList.insertRec.eq_1", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Eq.mpr", "Eq.refl", "List.nil", "List.nodupKeys_nil", "Membership.mem", "Not", "Sigma", "con...
null
false
false
theorem
Mathlib.Data.List.AList
AList.insertRec_insert
AList
null
109
[ "AList", "AList.insert", "AList.insertRec", "AList.instEmptyCollection", "AList.instMembership", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Membership.mem", "Not", "Sigma", "Sigma.fst", "Sigma.snd" ]
2,250
[ "AList", "AList.casesOn", "AList.entries", "AList.insert", "AList.insertRec", "AList.insertRec._proof_5", "AList.insertRec._proof_6", "AList.insertRec.eq_2", "AList.insert_of_notMem", "AList.instEmptyCollection", "AList.instMembership", "AList.mk", "AList.nodupKeys", "And", "And.intro", ...
null
false
false
theorem
Mathlib.Data.List.AList
AList.insertRec_insert_mk
AList
null
102
[ "AList", "AList.insert", "AList.insertRec", "AList.instEmptyCollection", "AList.instMembership", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Membership.mem", "Not" ]
95
[ "AList", "AList.insert", "AList.insertRec_insert", "AList.instEmptyCollection", "AList.instMembership", "DecidableEq", "EmptyCollection.emptyCollection", "Membership.mem", "Not", "Sigma.mk" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.insert_empty
AList
null
41
[ "AList", "AList.insert", "AList.instEmptyCollection", "AList.singleton", "DecidableEq", "EmptyCollection.emptyCollection", "Eq" ]
35
[ "AList", "AList.insert", "AList.instEmptyCollection", "DecidableEq", "EmptyCollection.emptyCollection", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.insert_insert
AList
null
40
[ "AList", "AList.insert", "DecidableEq", "Eq" ]
128
[ "AList", "AList.entries", "AList.ext", "AList.insert", "DecidableEq", "Eq", "Eq.trans", "List", "List.cons", "List.kerase", "List.kerase_cons_eq", "Sigma", "Sigma.mk", "True", "congrArg", "congrFun'", "eq_self", "of_eq_true" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.insert_insert_of_ne
AList
null
56
[ "AList", "AList.entries", "AList.insert", "DecidableEq", "List.Perm", "Ne", "Sigma" ]
230
[ "AList", "AList.entries", "AList.insert", "DecidableEq", "Eq", "Eq.mpr", "List", "List.Perm", "List.Perm.swap", "List.cons", "List.kerase", "List.kerase_comm", "List.kerase_cons_ne", "Ne", "Ne.symm", "Sigma", "Sigma.mk", "congrArg", "id" ]
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.insert_lookupFinsupp
AList
null
53
[ "AList", "AList.insert", "AList.lookupFinsupp", "DecidableEq", "Eq", "Finsupp", "Finsupp.update", "Zero" ]
386
[ "AList", "AList.insert", "AList.lookup", "AList.lookupFinsupp", "AList.lookupFinsupp_apply", "AList.lookup_insert", "AList.lookup_insert_ne", "DFunLike.coe", "DecidableEq", "Eq", "Eq.trans", "False", "Finsupp", "Finsupp.coe_update", "Finsupp.ext", "Finsupp.instFunLike", "Finsupp.upda...
null
false
false
theorem
Mathlib.Data.List.AList
AList.insert_of_notMem
AList
null
120
[ "AList", "AList.entries", "AList.insert", "AList.instMembership", "AList.mk", "AList.nodupKeys", "And", "And.intro", "DecidableEq", "Eq", "Iff.mpr", "List", "List.NodupKeys", "List.cons", "List.instMembership", "List.keys", "List.nodupKeys_cons", "Membership.mem", "Not", "Sigma...
128
[ "AList", "AList.entries", "AList.entries_insert_of_notMem", "AList.ext", "AList.insert", "AList.instMembership", "AList.mk", "AList.nodupKeys", "And", "And.intro", "DecidableEq", "Iff.mpr", "List", "List.NodupKeys", "List.cons", "List.instMembership", "List.keys", "List.nodupKeys_c...
null
false
false
theorem
Mathlib.Data.List.AList
AList.insert_singleton_eq
AList
null
39
[ "AList", "AList.insert", "AList.singleton", "DecidableEq", "Eq" ]
126
[ "AList.entries", "AList.ext", "AList.insert", "AList.singleton", "DecidableEq", "Eq", "Eq.trans", "List", "List.cons", "List.kerase", "List.kerase_cons_eq", "List.nil", "Sigma", "Sigma.mk", "True", "congrArg", "congrFun'", "eq_self", "of_eq_true" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.insert_union
AList
null
53
[ "AList", "AList.insert", "AList.instUnion", "DecidableEq", "Eq", "Union.union" ]
294
[ "AList", "AList.entries", "AList.ext", "AList.insert", "AList.instUnion", "DecidableEq", "Eq", "Eq.trans", "GetElem?.getElem?", "Iff", "LT.lt", "List", "List.cons", "List.ext_getElem?", "List.instGetElem?NatLtLength", "List.kerase", "List.kunion", "List.kunion_kerase", "List.leng...
5
false
false
definition
Mathlib.Data.List.AList
AList.instDecidableEq
AList
regular
22
[ "AList", "DecidableEq" ]
80
[ "AList", "AList.entries", "AList.instDecidableEq._proof_1", "Decidable", "DecidableEq", "Eq", "Eq.mpr", "List", "Sigma", "Sigma.instDecidableEqSigma", "inferInstance", "instDecidableEqList" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.instDecidableEq._proof_1
AList.instDecidableEq
null
44
[ "AList", "AList.entries", "Decidable", "Eq", "List", "Sigma" ]
69
[ "AList", "AList.entries", "AList.ext_iff", "Decidable", "Eq", "List", "Sigma", "congrArg", "id", "propext" ]
5
false
false
definition
Mathlib.Data.List.AList
AList.instDecidableMem
AList
regular
31
[ "AList", "AList.instMembership", "Decidable", "DecidableEq", "Membership.mem" ]
59
[ "AList", "AList.instMembership", "AList.lookup", "AList.lookup_isSome", "Bool", "Bool.true", "DecidableEq", "Eq", "Membership.mem", "Option.isSome", "decidable_of_iff", "instDecidableEqBool" ]
1
false
false
definition
Mathlib.Data.List.AList
AList.instEmptyCollection
AList
regular
12
[ "AList", "EmptyCollection" ]
26
[ "AList", "AList.mk", "EmptyCollection.mk", "List.nil", "List.nodupKeys_nil", "Sigma" ]
2
false
false
definition
Mathlib.Data.List.AList
AList.instInhabited
AList
regular
12
[ "AList", "Inhabited" ]
19
[ "AList", "AList.instEmptyCollection", "EmptyCollection.emptyCollection", "Inhabited.mk" ]
4
false
false
definition
Mathlib.Data.List.AList
AList.instMembership
AList
regular
13
[ "AList", "Membership" ]
32
[ "AList", "AList.keys", "List", "List.instMembership", "Membership.mem", "Membership.mk" ]
6
false
false
definition
Mathlib.Data.List.AList
AList.instUnion
AList
regular
16
[ "AList", "DecidableEq", "Union" ]
21
[ "AList", "AList.union", "DecidableEq", "Union.mk" ]
3
false
false
definition
Mathlib.Data.List.AList
AList.keys
AList
regular
14
[ "AList", "List" ]
20
[ "AList", "AList.entries", "List.keys" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.keys.eq_1
AList.keys
null
30
[ "AList", "AList.entries", "AList.keys", "Eq", "List", "List.keys" ]
21
[ "AList", "AList.keys", "Eq.refl", "List" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_empty
AList
null
28
[ "AList", "AList.instEmptyCollection", "AList.keys", "EmptyCollection.emptyCollection", "Eq", "List", "List.nil" ]
25
[ "AList", "AList.instEmptyCollection", "AList.keys", "EmptyCollection.emptyCollection", "List", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_erase
AList
null
43
[ "AList", "AList.erase", "AList.keys", "DecidableEq", "Eq", "List", "List.erase", "instBEqOfDecidableEq" ]
28
[ "AList", "AList.entries", "DecidableEq", "List.keys_kerase" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_insert
AList
null
51
[ "AList", "AList.insert", "AList.keys", "DecidableEq", "Eq", "List", "List.cons", "List.erase", "instBEqOfDecidableEq" ]
108
[ "AList", "AList.entries", "AList.insert", "AList.keys", "DecidableEq", "Eq", "Eq.trans", "List", "List.cons", "List.erase", "List.kerase", "List.keys", "List.keys_kerase", "True", "congrArg", "congrFun'", "eq_self", "instBEqOfDecidableEq", "of_eq_true" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_mk
AList
null
39
[ "AList.keys", "AList.mk", "Eq", "List", "List.NodupKeys", "List.keys", "Sigma" ]
34
[ "AList.keys", "AList.mk", "List", "List.NodupKeys", "Sigma", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_nodup
AList
null
19
[ "AList", "AList.keys", "List.Nodup" ]
16
[ "AList", "AList.nodupKeys" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_replace
AList
null
39
[ "AList", "AList.keys", "AList.replace", "DecidableEq", "Eq", "List" ]
32
[ "AList", "AList.entries", "DecidableEq", "List.keys_kreplace" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_singleton
AList
null
33
[ "AList.keys", "AList.singleton", "Eq", "List", "List.cons", "List.nil" ]
26
[ "AList.keys", "AList.singleton", "List", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.keys_subset_keys_of_entries_subset_entries
AList
null
49
[ "AList", "AList.entries", "AList.keys", "HasSubset.Subset", "List", "List.instHasSubset", "Sigma" ]
352
[ "AList", "AList.entries", "AList.instMembership", "AList.keys", "AList.lookup", "AList.lookup_isSome", "AList.mem_keys", "AList.mem_lookup_iff", "Bool", "Bool.true", "Classical.decEq", "DecidableEq", "Eq", "Eq.mp", "Eq.mpr", "Eq.symm", "HasSubset.Subset", "Iff.mp", "Iff.mpr", "...
4
false
false
definition
Mathlib.Data.List.AList
AList.lookup
AList
regular
20
[ "AList", "DecidableEq", "Option" ]
28
[ "AList", "AList.entries", "DecidableEq", "List.dlookup" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.lookup.congr_simp
AList.lookup
null
49
[ "AList", "AList.lookup", "DecidableEq", "Eq", "Option" ]
130
[ "AList", "AList.lookup", "Decidable", "DecidableEq", "Eq", "Eq.ndrec", "Eq.rec", "Eq.refl", "Option", "Pi.instSubsingleton", "Subsingleton.elim", "instSubsingletonDecidable" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.lookup.eq_1
AList.lookup
null
41
[ "AList", "AList.entries", "AList.lookup", "DecidableEq", "Eq", "List.dlookup", "Option" ]
30
[ "AList", "AList.lookup", "DecidableEq", "Eq.refl", "Option" ]
9
false
false
definition
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp
AList
regular
20
[ "AList", "Finsupp", "Zero" ]
97
[ "AList", "AList.entries", "AList.lookup", "AList.lookupFinsupp._proof_5", "Classical.decEq", "Decidable.decide", "Eq", "Finsupp.mk", "List.filter", "List.keys", "List.toFinset", "Ne", "OfNat.ofNat", "Option.getD", "Sigma", "Sigma.snd", "Zero", "Zero.toOfNat0", "instDecidableNot" ...
null
true
true
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp._proof_5
AList.lookupFinsupp
null
108
[ "AList", "AList.entries", "AList.lookup", "Classical.decEq", "Decidable.decide", "Eq", "Finset", "Finset.instSetLike", "Iff", "List.filter", "List.keys", "List.toFinset", "Membership.mem", "Ne", "OfNat.ofNat", "Option.getD", "SetLike.instMembership", "Sigma", "Sigma.snd", "Zero...
921
[ "AList", "AList.entries", "AList.lookup", "And", "Bool", "Bool.false", "Bool.not", "Bool.not_eq_eq_eq_not._simp_1", "Bool.not_true", "Bool.true", "Classical.decEq", "Classical.propDecidable", "Decidable.decide", "Eq", "Eq.mpr", "Eq.ndrec", "Eq.refl", "Eq.symm", "Eq.trans", "Exi...
null
true
false
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp.eq_1
AList.lookupFinsupp
null
110
[ "AList", "AList.entries", "AList.lookup", "AList.lookupFinsupp", "AList.lookupFinsupp._proof_5", "Classical.decEq", "Decidable.decide", "Eq", "Finsupp", "Finsupp.mk", "List.filter", "List.keys", "List.toFinset", "Ne", "OfNat.ofNat", "Option.getD", "Sigma", "Sigma.snd", "Zero", ...
28
[ "AList", "AList.lookupFinsupp", "Eq.refl", "Finsupp", "Zero" ]
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp_apply
AList
null
65
[ "AList", "AList.lookup", "AList.lookupFinsupp", "DFunLike.coe", "DecidableEq", "Eq", "Finsupp", "Finsupp.instFunLike", "OfNat.ofNat", "Option.getD", "Zero", "Zero.toOfNat0" ]
274
[ "AList", "AList.lookup", "AList.lookupFinsupp", "Classical.decEq", "DFunLike.coe", "Decidable", "DecidableEq", "Eq", "Eq.ndrec", "Eq.rec", "Eq.refl", "Finsupp", "Finsupp.instFunLike", "OfNat.ofNat", "Option", "Option.getD", "Pi.instSubsingleton", "Subsingleton.elim", "Zero", "Z...
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp_eq_iff_of_ne_zero
AList
null
82
[ "AList", "AList.lookup", "AList.lookupFinsupp", "DFunLike.coe", "DecidableEq", "Eq", "Finsupp", "Finsupp.instFunLike", "Iff", "Membership.mem", "Ne", "OfNat.ofNat", "Option", "Option.instMembership", "Zero", "Zero.toOfNat0" ]
283
[ "AList", "AList.lookup", "AList.lookupFinsupp", "AList.lookupFinsupp_apply", "DFunLike.coe", "DecidableEq", "Eq", "Eq.mpr", "Eq.trans", "False", "False.elim", "Finsupp", "Finsupp.instFunLike", "Iff", "Membership.mem", "Ne", "Ne.symm", "OfNat.ofNat", "Option", "Option.casesOn", ...
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp_eq_zero_iff
AList
null
90
[ "AList", "AList.instMembership", "AList.lookup", "AList.lookupFinsupp", "DFunLike.coe", "DecidableEq", "Eq", "Finsupp", "Finsupp.instFunLike", "Iff", "Membership.mem", "Not", "OfNat.ofNat", "Option", "Option.instMembership", "Or", "Zero", "Zero.toOfNat0" ]
396
[ "AList", "AList.instMembership", "AList.lookup", "AList.lookupFinsupp", "AList.lookupFinsupp_apply", "AList.lookup_eq_none", "DFunLike.coe", "DecidableEq", "Eq", "Eq.mpr", "Eq.symm", "Eq.trans", "False", "False.elim", "Finsupp", "Finsupp.instFunLike", "Iff", "Membership.mem", "No...
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp_support
AList
null
90
[ "AList", "AList.entries", "AList.lookupFinsupp", "Decidable.decide", "DecidableEq", "Eq", "Finset", "Finsupp.support", "List.filter", "List.keys", "List.toFinset", "Ne", "OfNat.ofNat", "Sigma", "Sigma.snd", "Zero", "Zero.toOfNat0", "instDecidableNot" ]
743
[ "AList", "AList.entries", "AList.lookupFinsupp", "Bool", "Classical.decEq", "Decidable", "Decidable.decide", "DecidableEq", "Eq", "Eq.casesOn", "Eq.ndrec", "Eq.refl", "Eq.symm", "Finset", "Finsupp.support", "HEq", "HEq.refl", "Lean.Meta.FastSubsingleton.elim", "Lean.Meta.instFast...
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.lookupFinsupp_surjective
AList
null
26
[ "AList", "AList.lookupFinsupp", "Finsupp", "Function.Surjective", "Zero" ]
49
[ "AList", "AList.lookupFinsupp", "Eq", "Exists.intro", "Finsupp", "Finsupp.toAList", "Finsupp.toAList_lookupFinsupp", "Zero" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_empty
AList
null
37
[ "AList", "AList.instEmptyCollection", "AList.lookup", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Option", "Option.none" ]
34
[ "AList", "AList.instEmptyCollection", "AList.lookup", "DecidableEq", "EmptyCollection.emptyCollection", "Option", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_eq_none
AList
null
49
[ "AList", "AList.instMembership", "AList.lookup", "DecidableEq", "Eq", "Iff", "Membership.mem", "Not", "Option", "Option.none" ]
28
[ "AList", "AList.entries", "DecidableEq", "List.dlookup_eq_none" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_erase
AList
null
39
[ "AList", "AList.erase", "AList.lookup", "DecidableEq", "Eq", "Option", "Option.none" ]
33
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.dlookup_kerase" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_erase_ne
AList
null
46
[ "AList", "AList.erase", "AList.lookup", "DecidableEq", "Eq", "Ne", "Option" ]
38
[ "AList", "AList.entries", "DecidableEq", "List.dlookup_kerase_ne", "Ne" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_insert
AList
null
44
[ "AList", "AList.insert", "AList.lookup", "DecidableEq", "Eq", "Option", "Option.some" ]
87
[ "AList", "AList.entries", "AList.insert", "AList.lookup", "DecidableEq", "Eq", "Eq.trans", "List.dlookup_kinsert", "Option", "Option.some", "True", "congrArg", "congrFun'", "eq_self", "of_eq_true" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_insert_eq_none
AList
null
58
[ "AList", "AList.insert", "AList.lookup", "And", "DecidableEq", "Eq", "Iff", "Ne", "Option", "Option.none" ]
392
[ "AList", "AList.insert", "AList.lookup", "AList.lookup_insert", "AList.lookup_insert_ne", "And", "DecidableEq", "Eq", "Eq.ndrec", "Eq.trans", "False", "False.elim", "Iff", "Ne", "Not", "Option", "Option.ctorIdx", "Option.none", "Option.some", "True", "congr", "congrArg", ...
null
true
true
theorem
Mathlib.Data.List.AList
AList.lookup_insert_eq_none._simp_1
AList.lookup_insert_eq_none
null
60
[ "AList", "AList.insert", "AList.lookup", "And", "DecidableEq", "Eq", "Ne", "Option", "Option.none" ]
67
[ "AList", "AList.insert", "AList.lookup", "AList.lookup_insert_eq_none", "And", "DecidableEq", "Eq", "Ne", "Option", "Option.none", "propext" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_insert_ne
AList
null
50
[ "AList", "AList.insert", "AList.lookup", "DecidableEq", "Eq", "Ne", "Option" ]
42
[ "AList", "AList.entries", "DecidableEq", "List.dlookup_kinsert_ne", "Ne" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_isSome
AList
null
48
[ "AList", "AList.instMembership", "AList.lookup", "Bool", "Bool.true", "DecidableEq", "Eq", "Iff", "Membership.mem", "Option.isSome" ]
28
[ "AList", "AList.entries", "DecidableEq", "List.dlookup_isSome" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_to_alist
AList
null
44
[ "AList.lookup", "DecidableEq", "Eq", "List", "List.dlookup", "List.toAList", "Option", "Sigma" ]
162
[ "AList", "AList.entries", "AList.lookup", "AList.lookup.eq_1", "AList.mk", "DecidableEq", "Eq", "Eq.mpr", "Eq.refl", "List", "List.dedupKeys", "List.dlookup", "List.dlookup_dedupKeys", "List.nodupKeys_dedupKeys", "List.toAList", "List.toAList.eq_1", "Option", "Sigma", "congrArg",...
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_union_eq_some
AList
null
78
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "And", "DecidableEq", "Eq", "Iff", "Membership.mem", "Not", "Option", "Option.some", "Or", "Union.union" ]
38
[ "AList", "AList.entries", "DecidableEq", "List.mem_dlookup_kunion" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.lookup_union_eq_some._simp_1
AList.lookup_union_eq_some
null
80
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "And", "DecidableEq", "Eq", "Membership.mem", "Not", "Option", "Option.some", "Or", "Union.union" ]
87
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "AList.lookup_union_eq_some", "And", "DecidableEq", "Eq", "Membership.mem", "Not", "Option", "Option.some", "Or", "Union.union", "propext" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_union_left
AList
null
60
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "DecidableEq", "Eq", "Membership.mem", "Option", "Union.union" ]
34
[ "AList", "AList.entries", "DecidableEq", "List.dlookup_kunion_left" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.lookup_union_right
AList
null
62
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "DecidableEq", "Eq", "Membership.mem", "Not", "Option", "Union.union" ]
34
[ "AList", "AList.entries", "DecidableEq", "List.dlookup_kunion_right" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_erase
AList
null
53
[ "AList", "AList.erase", "AList.instMembership", "And", "DecidableEq", "Iff", "Membership.mem", "Ne" ]
226
[ "AList", "AList.erase", "AList.instMembership", "AList.keys", "AList.keys_erase", "AList.keys_nodup", "AList.mem_keys", "And", "DecidableEq", "Eq", "Eq.mpr", "Eq.symm", "Iff", "Iff.rfl", "List", "List.Nodup.mem_erase_iff", "List.erase", "List.instMembership", "Membership.mem", ...
null
true
true
theorem
Mathlib.Data.List.AList
AList.mem_erase._simp_1
AList.mem_erase
null
55
[ "AList", "AList.erase", "AList.instMembership", "And", "DecidableEq", "Eq", "Membership.mem", "Ne" ]
61
[ "AList", "AList.erase", "AList.instMembership", "AList.mem_erase", "And", "DecidableEq", "Membership.mem", "Ne", "propext" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_insert
AList
null
57
[ "AList", "AList.insert", "AList.instMembership", "DecidableEq", "Eq", "Iff", "Membership.mem", "Or" ]
35
[ "AList", "AList.entries", "DecidableEq", "List.mem_keys_kinsert" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.mem_insert._simp_1
AList.mem_insert
null
59
[ "AList", "AList.insert", "AList.instMembership", "DecidableEq", "Eq", "Membership.mem", "Or" ]
66
[ "AList", "AList.insert", "AList.instMembership", "AList.mem_insert", "DecidableEq", "Eq", "Membership.mem", "Or", "propext" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_keys
AList
null
42
[ "AList", "AList.instMembership", "AList.keys", "Iff", "List", "List.instMembership", "Membership.mem" ]
27
[ "AList", "AList.instMembership", "Iff.rfl", "Membership.mem" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_lookup_iff
AList
null
63
[ "AList", "AList.entries", "AList.lookup", "DecidableEq", "Iff", "List", "List.instMembership", "Membership.mem", "Option", "Option.instMembership", "Sigma", "Sigma.mk" ]
37
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.mem_dlookup_iff" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_lookup_union
AList
null
79
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "And", "DecidableEq", "Iff", "Membership.mem", "Not", "Option", "Option.instMembership", "Or", "Union.union" ]
38
[ "AList", "AList.entries", "DecidableEq", "List.mem_dlookup_kunion" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_lookup_union_middle
AList
null
98
[ "AList", "AList.instMembership", "AList.instUnion", "AList.lookup", "DecidableEq", "Membership.mem", "Not", "Option", "Option.instMembership", "Union.union" ]
44
[ "AList", "AList.entries", "DecidableEq", "List.mem_dlookup_kunion_middle" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_mk
AList
null
56
[ "AList", "AList.instMembership", "AList.mk", "Iff", "List", "List.NodupKeys", "List.instMembership", "List.keys", "Membership.mem", "Sigma" ]
41
[ "AList", "AList.instMembership", "AList.mk", "Iff.rfl", "List", "List.NodupKeys", "Membership.mem", "Sigma" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.mem_mk._simp_1
AList.mem_mk
null
58
[ "AList", "AList.instMembership", "AList.mk", "Eq", "List", "List.NodupKeys", "List.instMembership", "List.keys", "Membership.mem", "Sigma" ]
63
[ "AList", "AList.instMembership", "AList.mem_mk", "AList.mk", "List", "List.NodupKeys", "List.instMembership", "List.keys", "Membership.mem", "Sigma", "propext" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_of_perm
AList
null
48
[ "AList", "AList.entries", "AList.instMembership", "Iff", "List.Perm", "Membership.mem", "Sigma" ]
60
[ "AList", "AList.entries", "List.Perm", "List.Perm.map", "List.Perm.mem_iff", "List.map", "Sigma", "Sigma.fst" ]