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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
null | false | false | theorem | Mathlib.Analysis.Normed.Field.WithAbs | AbsoluteValue.Completion.locallyCompactSpace | AbsoluteValue.Completion | null | 236 | [
"AbsoluteValue",
"AbsoluteValue.Completion",
"CompleteSpace",
"DFunLike.coe",
"DivisionSemiring.toSemiring",
"EMetricSpace.toPseudoEMetricSpace",
"Field",
"Field.toSemifield",
"Isometry",
"LocallyCompactSpace",
"MetricSpace.toEMetricSpace",
"NormedCommRing.toSeminormedCommRing",
"NormedField... | 389 | [
"AbsoluteValue",
"CompletableTopField.toT0Space",
"CompleteSpace",
"CompletelyNormalSpace.toNormalSpace",
"DFunLike.coe",
"DivisionSemiring.toSemiring",
"EMetric.instIsCountablyGeneratedUniformity",
"EMetricSpace.metrizableSpace",
"EMetricSpace.toPseudoEMetricSpace",
"Field",
"Field.toSemifield"... |
null | false | false | inductive | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible | AbsoluteValue | null | 33 | [
"AbsoluteValue",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] | null | [] |
null | true | true | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible._sizeOf_1 | AbsoluteValue.IsAdmissible | abbrev | 43 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"Nat",
"SemilatticeInf.toPartialOrder",
"SizeOf",
"instLatticeInt"
] | 270 | [
"AbsoluteValue",
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"AbsoluteValue.IsAdmissible.rec",
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"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucl... |
null | true | true | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible._sizeOf_inst | AbsoluteValue.IsAdmissible | abbrev | 43 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"SizeOf",
"instLatticeInt"
] | 52 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible._sizeOf_1",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"SizeOf",
"Siz... |
null | false | false | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.card | AbsoluteValue.IsAdmissible | abbrev | 41 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"Nat",
"Real",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] | 39 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] |
null | true | false | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.casesOn | AbsoluteValue.IsAdmissible | abbrev | 242 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucli... | 353 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsAdmissible.rec",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring"... |
17 | true | false | definition | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.ctorIdx | AbsoluteValue.IsAdmissible | regular | 39 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"Nat",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] | 39 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] |
null | false | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.exists_approx | AbsoluteValue.IsAdmissible | null | 278 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"And",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDom... | 1,862 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
"AbsoluteValue.IsAdmissible.exists_approx_aux",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"And",
"And.casesOn",
"And.intro",
"CommRing.toCommSemiring",
"CommRing.toRing",
... |
null | false | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.exists_approx_aux | AbsoluteValue.IsAdmissible | null | 266 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"And",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDom... | 3,411 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
"AbsoluteValue.IsAdmissible.exists_partition",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"And",
"And.casesOn",
"And.intro",
"And.right",
"Classical.decEq",
"CommRing.toCo... |
null | false | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.exists_partition | AbsoluteValue.IsAdmissible | null | 223 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
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"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"EuclideanDomain",
"EuclideanDoma... | 1,521 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
"AbsoluteValue.IsAdmissible.exists_partition'",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike",... |
null | false | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.exists_partition' | AbsoluteValue.IsAdmissible | null | 223 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.card",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"EuclideanDomain",
"EuclideanDoma... | 39 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] |
null | false | false | constructor | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.mk | AbsoluteValue.IsAdmissible | null | 225 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"EuclideanDomain",
"EuclideanDomain.ins... | null | [] |
null | true | true | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.mk._flat_ctor | AbsoluteValue.IsAdmissible.mk | abbrev | 262 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"EuclideanDomain",
"EuclideanDomain.instMod",
"EuclideanDomain.r",
... | 273 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"EuclideanDomain",
"EuclideanDoma... |
null | true | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.mk.inj | AbsoluteValue.IsAdmissible.mk | null | 344 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucli... | 358 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsAdmissible.mk.noConfusion",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.... |
null | true | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.mk.injEq | AbsoluteValue.IsAdmissible.mk | null | 347 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
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"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucli... | 581 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsAdmissible.mk.inj",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiri... |
null | true | false | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.mk.noConfusion | AbsoluteValue.IsAdmissible.mk | abbrev | 348 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucli... | 404 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsAdmissible.noConfusion",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toS... |
null | true | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.mk.sizeOf_spec | AbsoluteValue.IsAdmissible.mk | null | 276 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible._sizeOf_inst",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.to... | 256 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eq.refl",
"EuclideanDomain",
"EuclideanDomain.instMod",
"Euclidean... |
null | true | false | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.noConfusion | AbsoluteValue.IsAdmissible | abbrev | 116 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.noConfusionType",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"Eq",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"HEq",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrd... | 637 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.casesOn",
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"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSem... |
null | true | false | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.noConfusionType | AbsoluteValue.IsAdmissible | abbrev | 44 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] | 361 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.casesOn",
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"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"... |
null | false | false | recursor | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.rec | AbsoluteValue.IsAdmissible | null | 241 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucli... | null | [] |
null | true | false | abbrev | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.recOn | AbsoluteValue.IsAdmissible | abbrev | 242 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"Eucli... | 249 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsAdmissible.rec",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring"... |
null | true | false | theorem | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | AbsoluteValue.IsAdmissible.toIsEuclidean | AbsoluteValue.IsAdmissible | null | 46 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.IsEuclidean",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] | 39 | [
"AbsoluteValue",
"AbsoluteValue.IsAdmissible",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"Int",
"Int.instSemiring",
"Lattice.toSemilatticeInf",
"SemilatticeInf.toPartialOrder",
"instLatticeInt"
] |
3 | false | false | definition | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv | AbsoluteValue | regular | 33 | [
"AbsoluteValue",
"PartialOrder",
"Semiring"
] | 76 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.eq_iff_eq | AbsoluteValue.IsEquiv | null | 79 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Eq",
"Iff",
"PartialOrder",
"Semiring"
] | 167 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"And",
"DFunLike.coe",
"Eq",
"Eq.trans",
"Iff",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",
"True",
"_private.Mathlib.Analysis.AbsoluteValue.Equivalence.0.AbsoluteValue.IsEquiv.eq_iff_... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.eq_one_iff | AbsoluteValue.IsEquiv | null | 104 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq",
"Iff",
"IsDomain",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nontrivial",
"OfNat.ofNat",
"One.toOfNat1",
"PartialOrder",
"Semiri... | 226 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.eq_iff_eq",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq",
"Eq.mp",
"Iff",
"IsDomain",
"MonoidHomClass.toOneHomClass",... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero | AbsoluteValue.IsEquiv | null | 280 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"DFunLike.coe",
"Distrib.toAdd",
"Distrib.toMul",
"DivisionSemiring.toSemiring",
"EquivLike.toFunLike",
"Field",
"Field.toSemifield",
"Filter",
"Filter.instMembership",
"Membership.mem",
"MulZeroClass.toZero",
"NormedCommRing.toSeminormedCommRing",... | 2,026 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AbsoluteValue.isEquiv_iff_exists_rpow_eq",
"AbsoluteValue.nonneg",
"AddGroup.toSubtractionMonoid",
"And",
"And.casesOn",
"And.intro",
"DFunLike.coe",
"Dist.dist",
"Distrib.toAdd",
"Distrib.toMul",
"DivisionRing.toRing",
... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs | AbsoluteValue.IsEquiv | null | 194 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"DFunLike.coe",
"Distrib.toAdd",
"Distrib.toMul",
"DivisionSemiring.toSemiring",
"EquivLike.toFunLike",
"Field",
"Field.toSemifield",
"NormedCommRing.toSeminormedCommRing",
"NormedField.toNormedCommRing",
"PseudoMetricSpace.toUniformSpace",
"Real",
... | 1,895 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero",
"AbsoluteValue.IsEquiv.symm",
"AddGroup.toSubtractionMonoid",
"AddGroupWithOne.toAddGroup",
"And",
"And.casesOn",
"And.intro",
"ChainCompletePartialOrder.instOfCompleteLattice",
"ChainCompletePart... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.isNontrivial | AbsoluteValue.IsEquiv | null | 67 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsNontrivial",
"IsDomain",
"Nontrivial",
"PartialOrder",
"Semiring"
] | 75 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.isNontrivial_congr",
"AbsoluteValue.IsNontrivial",
"Iff.mp",
"IsDomain",
"Nontrivial",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.isNontrivial_congr | AbsoluteValue.IsEquiv | null | 63 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsNontrivial",
"Iff",
"IsDomain",
"Nontrivial",
"PartialOrder",
"Semiring"
] | 314 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.eq_one_iff",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq",
"Eq.refl",
"Eq.trans",
"Iff",
"Iff.mp",
"IsDomain",
"MulZeroClas... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.le_iff_le | AbsoluteValue.IsEquiv | null | 86 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring"
] | 48 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.le_one_iff | AbsoluteValue.IsEquiv | null | 111 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Iff",
"IsDomain",
"LE.le",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nontrivial",
"OfNat.ofNat",
"One.toOfNat1",
"PartialOrder",
"Par... | 224 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq.mp",
"Iff",
"IsDomain",
"LE.le",
"MonoidHomClass.toOneHomClass",
"MonoidWithZeroHomClass.toMonoi... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.log_div_log_eq_log_div_log | AbsoluteValue.IsEquiv | null | 225 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"DivInvMonoid.toDiv",
"DivisionSemiring.toSemiring",
"Eq",
"Field",
"Field.toSemifield",
"HDiv.hDiv",
"MulZeroClass.toZero",
"Ne",
"OfNat.ofNat",
"One.toOfNat1",
"Real",
"Real.instDivInvMonoid",
"Real.... | 4,130 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.lt_one_iff",
"AbsoluteValue.IsEquiv.one_lt_iff",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AbsoluteValue.pos",
"AddCommGroup.toDivisionAddCommMonoid",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddGroup.toSub... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.log_div_log_pos | AbsoluteValue.IsEquiv | null | 178 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"DivInvMonoid.toDiv",
"DivisionSemiring.toSemiring",
"Field",
"Field.toSemifield",
"HDiv.hDiv",
"LT.lt",
"MulZeroClass.toZero",
"Ne",
"OfNat.ofNat",
"One.toOfNat1",
"Real",
"Real.instDivInvMonoid",
"Re... | 527 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.lt_one_iff",
"AbsoluteValue.IsEquiv.one_lt_iff",
"AbsoluteValue.funLike",
"AbsoluteValue.pos",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddGroup.addLeftReflectLE_of_addLeftMono",
"AddGroup.toSubNegMonoid",
"AddGroup.toSubtractionM... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.lt_iff_lt | AbsoluteValue.IsEquiv | null | 86 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
"Semiring"
] | 88 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"PartialOrder",
"PartialOrder.toPreorder",
"Semiring",
"lt_iff_lt_of_le_iff_le'"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.lt_one_iff | AbsoluteValue.IsEquiv | null | 111 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Iff",
"IsDomain",
"LT.lt",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nontrivial",
"OfNat.ofNat",
"One.toOfNat1",
"PartialOrder",
"Par... | 233 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.lt_iff_lt",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq.mp",
"Iff",
"IsDomain",
"LT.lt",
"MonoidHomClass.toOneHomClas... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.one_le_iff | AbsoluteValue.IsEquiv | null | 110 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Iff",
"IsDomain",
"LE.le",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nontrivial",
"OfNat.ofNat",
"One.toOfNat1",
"PartialOrder",
"Par... | 237 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq.mp",
"Iff",
"IsDomain",
"LE.le",
"MonoidHomClass.toOneHomClass",
"MonoidWithZeroHomClass.toMonoi... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.one_lt_iff | AbsoluteValue.IsEquiv | null | 110 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Iff",
"IsDomain",
"LT.lt",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nontrivial",
"OfNat.ofNat",
"One.toOfNat1",
"PartialOrder",
"Par... | 246 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsEquiv.lt_iff_lt",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Eq.mp",
"Iff",
"IsDomain",
"LT.lt",
"MonoidHomClass.toOneHomClas... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.refl | AbsoluteValue.IsEquiv | null | 34 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"PartialOrder",
"Semiring"
] | 63 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff.rfl",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.rfl | AbsoluteValue.IsEquiv | null | 34 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"PartialOrder",
"Semiring"
] | 63 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff.rfl",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.symm | AbsoluteValue.IsEquiv | null | 50 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"PartialOrder",
"Semiring"
] | 89 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff.symm",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.IsEquiv.trans | AbsoluteValue.IsEquiv | null | 66 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"PartialOrder",
"Semiring"
] | 114 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Iff.trans",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring"
] |
null | false | false | inductive | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean | AbsoluteValue | null | 35 | [
"AbsoluteValue",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"PartialOrder",
"Semiring"
] | null | [] |
null | true | false | abbrev | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.casesOn | AbsoluteValue.IsEuclidean | abbrev | 115 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.t... | 167 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.IsEuclidean.rec",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.map_lt_map_iff | AbsoluteValue.IsEuclidean | null | 93 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
"... | 58 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.map_lt_map_iff'",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.map_lt_map_iff' | AbsoluteValue.IsEuclidean | null | 93 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
"... | 44 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"EuclideanDomain",
"EuclideanDomain.toCommRing",
"PartialOrder",
"Semiring"
] |
null | true | true | theorem | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.map_lt_map_iff._simp_1 | AbsoluteValue.IsEuclidean.map_lt_map_iff | null | 95 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Eq",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
"S... | 104 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.map_lt_map_iff",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"LT.lt",
"PartialOrder",
"PartialOrde... |
null | false | false | constructor | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.mk | AbsoluteValue.IsEuclidean | null | 92 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
"... | null | [] |
null | true | true | abbrev | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.mk._flat_ctor | AbsoluteValue.IsEuclidean.mk | abbrev | 92 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
"... | 93 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLT",
... |
null | false | false | recursor | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.rec | AbsoluteValue.IsEuclidean | null | 114 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.t... | null | [] |
null | true | false | abbrev | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.recOn | AbsoluteValue.IsEuclidean | abbrev | 115 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
"PartialOrder",
"PartialOrder.t... | 124 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.IsEuclidean.rec",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.r",
"EuclideanDomain.toCommRing",
"Iff",
"LT.lt",
... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.IsEuclidean.sub_mod_lt | AbsoluteValue.IsEuclidean | null | 124 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.instMod",
"EuclideanDomain.toCommRing",
"HMod.hMod",
"LT.lt",
"MulZeroClass.toZero",
"Ne",
"OfNat.ofNat",
"Part... | 150 | [
"AbsoluteValue",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.IsEuclidean.map_lt_map_iff",
"AbsoluteValue.funLike",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"EuclideanDomain",
"EuclideanDomain.instMod",
"EuclideanDomain.mod_lt",
"EuclideanDomain.r",
"EuclideanDomain... |
3 | false | false | definition | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.IsNontrivial | AbsoluteValue | regular | 26 | [
"AbsoluteValue",
"PartialOrder",
"Semiring"
] | 95 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"DFunLike.coe",
"Exists",
"MulZeroClass.toZero",
"Ne",
"NonAssocSemiring.toAddCommMonoidWithOne",
"OfNat.ofNat",
"One.toOfNat1",
"PartialOrder",
"Semiring",
"Semiring.toN... |
null | true | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.IsNontrivial.eq_1 | AbsoluteValue.IsNontrivial | null | 107 | [
"AbsoluteValue",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"DFunLike.coe",
"Eq",
"Exists",
"MulZeroClass.toZero",
"Ne",
"NonAssocSemiring.toAddCommMonoidWithOne",
"OfNat.ofNat",
"One.toOfNat1",
"Part... | 37 | [
"AbsoluteValue",
"AbsoluteValue.IsNontrivial",
"Eq.refl",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.IsNontrivial.exists_abv_gt_one | AbsoluteValue.IsNontrivial | null | 200 | [
"AbsoluteValue",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"DFunLike.coe",
"Distrib.toAdd",
"DistribLattice.toLattice",
"DivisionSemiring.toSemiring",
"Exists",
"ExistsAddOfLE",
"Field",
"Field.toSemifield",
... | 771 | [
"AbsoluteValue",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AbsoluteValue.pos",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"And.casesOn",
"CommGroupWithZero.toDivisionCommMonoid",
"DFunLike.coe",
"Distrib.toA... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.IsNontrivial.exists_abv_lt_one | AbsoluteValue.IsNontrivial | null | 221 | [
"AbsoluteValue",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"DFunLike.coe",
"Distrib.toAdd",
"DistribLattice.toLattice",
"DivisionSemiring.toSemiring",
"Exists",
"ExistsAddOfLE",
"Field",
"Field.toSemif... | 693 | [
"AbsoluteValue",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.IsNontrivial.exists_abv_gt_one",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AbsoluteValue.ne_zero_iff",
"AbsoluteValue.pos",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"And.intro... |
null | false | false | inductive | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver | AbsoluteValue | null | 83 | [
"AbsoluteValue",
"Algebra",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"IsSimpleRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing",
"Nontrivial",
"PartialOrder",
"Semiring"
] | null | [] |
null | true | false | abbrev | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver.casesOn | AbsoluteValue.LiesOver | abbrev | 185 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.LiesOver.mk",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCom... | 246 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.LiesOver.mk",
"AbsoluteValue.LiesOver.rec",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
... |
null | false | false | theorem | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver.comp_eq | AbsoluteValue.LiesOver | null | 150 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCommRing.toNonAssocRing",
"NonUn... | 99 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"Algebra",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"IsSimpleRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing",
"Nontrivial",
"PartialOr... |
null | true | false | theorem | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | AbsoluteValue.LiesOver.congr_simp | AbsoluteValue.LiesOver | null | 156 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"Algebra",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing",
"Nontrivial",
"P... | 242 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"Algebra",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"Eq.rec",
"Eq.refl",
"IsSimpleRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRi... |
null | false | false | constructor | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver.mk | AbsoluteValue.LiesOver | null | 150 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCommRing.toNonAssocRing",
"NonUn... | null | [] |
null | true | true | abbrev | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver.mk._flat_ctor | AbsoluteValue.LiesOver.mk | abbrev | 150 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCommRing.toNonAssocRing",
"NonUn... | 151 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver.mk",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCommRing.toNonAssocRing",
"No... |
null | false | false | recursor | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver.rec | AbsoluteValue.LiesOver | null | 184 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.LiesOver.mk",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCom... | null | [] |
null | true | false | abbrev | Mathlib.Analysis.Normed.Ring.WithAbs | AbsoluteValue.LiesOver.recOn | AbsoluteValue.LiesOver | abbrev | 185 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.LiesOver.mk",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
"IsSimpleRing",
"NonAssocCom... | 200 | [
"AbsoluteValue",
"AbsoluteValue.LiesOver",
"AbsoluteValue.LiesOver.mk",
"AbsoluteValue.LiesOver.rec",
"AbsoluteValue.comp",
"Algebra",
"Algebra.algebraMap",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Eq",
... |
3 | false | false | definition | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.Simps.apply | AbsoluteValue.Simps | regular | 27 | [
"AbsoluteValue",
"PartialOrder",
"Semiring"
] | 44 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"PartialOrder",
"Semiring"
] |
null | true | true | abbrev | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue._sizeOf_1 | AbsoluteValue | abbrev | 33 | [
"AbsoluteValue",
"Nat",
"PartialOrder",
"Semiring",
"SizeOf"
] | 258 | [
"AbsoluteValue",
"AbsoluteValue.rec",
"Distrib.toAdd",
"Distrib.toMul",
"Eq",
"HAdd.hAdd",
"Iff",
"LE.le",
"MulHom",
"MulHom._sizeOf_inst",
"MulHom.toFun",
"MulZeroClass.toZero",
"Nat",
"OfNat.ofNat",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",
"SizeOf... |
null | true | true | abbrev | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue._sizeOf_inst | AbsoluteValue | abbrev | 33 | [
"AbsoluteValue",
"PartialOrder",
"Semiring",
"SizeOf"
] | 46 | [
"AbsoluteValue",
"AbsoluteValue._sizeOf_1",
"PartialOrder",
"Semiring",
"SizeOf",
"SizeOf.mk"
] |
3 | false | false | definition | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs | AbsoluteValue | regular | 48 | [
"AbsoluteValue",
"DistribLattice.toLattice",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"instDistribLatticeOfLinearOrder"
] | 95 | [
"AbsoluteValue.abs._proof_1",
"AbsoluteValue.abs._proof_2",
"AbsoluteValue.abs._proof_3",
"AbsoluteValue.abs._proof_4",
"AbsoluteValue.mk",
"AddGroupWithOne.toAddGroup",
"Distrib.toMul",
"DistribLattice.toLattice",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"MulHom.mk",
... |
null | true | true | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs._proof_1 | AbsoluteValue.abs | null | 77 | [
"AddGroupWithOne.toAddGroup",
"Distrib.toMul",
"DistribLattice.toLattice",
"Eq",
"HMul.hMul",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toAddGroupWithOne",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"abs",
"instDistribLatticeOfLinearOrder",
... | 52 | [
"DistribLattice.toLattice",
"IsStrictOrderedRing",
"IsStrictOrderedRing.toIsOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"abs_mul",
"instDistribLatticeOfLinearOrder"
] |
null | true | true | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs._proof_2 | AbsoluteValue.abs | null | 84 | [
"AddGroup.toSubtractionMonoid",
"AddGroupWithOne.toAddGroup",
"DistribLattice.toLattice",
"IsStrictOrderedRing",
"LE.le",
"Lattice.toSemilatticeInf",
"LinearOrder",
"NegZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ring",
"Ring.toAddGroupWithOne",
"Ring.toS... | 105 | [
"AddCommMonoid.toAddCommSemigroup",
"AddGroupWithOne.toAddGroup",
"DistribLattice.toLattice",
"IsOrderedAddMonoid.toAddLeftMono",
"IsOrderedRing.toIsOrderedAddMonoid",
"IsStrictOrderedRing",
"IsStrictOrderedRing.toIsOrderedRing",
"LE.le",
"Lattice.toSemilatticeInf",
"LinearOrder",
"PartialOrder.... |
null | true | true | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs._proof_3 | AbsoluteValue.abs | null | 78 | [
"AddGroup.toSubtractionMonoid",
"AddGroupWithOne.toAddGroup",
"DistribLattice.toLattice",
"Eq",
"Iff",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"NegZeroClass.toZero",
"OfNat.ofNat",
"Ring",
"Ring.toAddGroupWithOne",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder... | 108 | [
"AddCommMonoid.toAddCommSemigroup",
"AddGroupWithOne.toAddGroup",
"DistribLattice.toLattice",
"IsOrderedAddMonoid.toAddLeftMono",
"IsOrderedRing.toIsOrderedAddMonoid",
"IsStrictOrderedRing",
"IsStrictOrderedRing.toIsOrderedRing",
"LE.le",
"Lattice.toSemilatticeInf",
"LinearOrder",
"PartialOrder.... |
null | true | true | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs._proof_4 | AbsoluteValue.abs | null | 95 | [
"AddCommGroup.toAddGroup",
"AddGroup.toSubNegMonoid",
"AddMonoid.toAddZeroClass",
"AddZero.toAdd",
"AddZeroClass.toAddZero",
"DistribLattice.toLattice",
"HAdd.hAdd",
"IsStrictOrderedRing",
"LE.le",
"Lattice.toSemilatticeInf",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ring... | 71 | [
"DistribLattice.toLattice",
"IsOrderedAddMonoid.toAddLeftMono",
"IsOrderedRing.toIsOrderedAddMonoid",
"IsStrictOrderedRing",
"IsStrictOrderedRing.toIsOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"PartialOrder.toPreorder",
"Ring",
"Ring.toAddCommGroup",
"Ring.toSemiring",
"Semilatti... |
null | true | false | theorem | Mathlib.Topology.UniformSpace.CompareReals | AbsoluteValue.abs.congr_simp | AbsoluteValue.abs | null | 57 | [
"AbsoluteValue",
"AbsoluteValue.abs",
"DistribLattice.toLattice",
"Eq",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"instDistribLatticeOfLinearOrder"
] | 56 | [
"AbsoluteValue",
"AbsoluteValue.abs",
"DistribLattice.toLattice",
"Eq.refl",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"instDistribLatticeOfLinearOrder"
] |
26 | false | false | definition | Mathlib.NumberTheory.ClassNumber.AdmissibleAbs | AbsoluteValue.absIsAdmissible | AbsoluteValue | regular | 14 | [
"AbsoluteValue.IsAdmissible",
"AbsoluteValue.abs",
"Int",
"Int.euclideanDomain",
"Int.instIsStrictOrderedRing",
"Int.instLinearOrder",
"Int.instRing"
] | 136 | [
"AbsoluteValue.IsAdmissible.mk",
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.abs",
"AbsoluteValue.abs_isEuclidean",
"AbsoluteValue.exists_partition_int",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DistribLattice.toLattice",
"DivInvMonoid.toDiv",
"EuclideanDomain.toCommRing",
"FloorRi... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs_abv_sub_le_abv_sub | AbsoluteValue | null | 167 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiring.toSemiring",
"DFunLike.coe",
"DistribLattice.toLattice",
"HSub.hSub",
"IsStrictOrderedRing",
"LE.le",
"Lattice.toSemila... | 337 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.le_sub",
"AbsoluteValue.map_sub",
"AddCommGroup.toAddGroup",
"AddGroup.existsAddOfLE",
"AddGroup.toSubNegMonoid",
"AddGroupWithOne.toAddGroup",
"And",
"And.intro",
"CommRing",
"CommRing.toCommSemiring",
"CommRing.toRing",
"CommSemiri... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.abs_apply | AbsoluteValue | null | 85 | [
"AbsoluteValue",
"AbsoluteValue.abs",
"AbsoluteValue.funLike",
"AddGroupWithOne.toAddGroup",
"DFunLike.coe",
"DistribLattice.toLattice",
"Eq",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toAddGroupWithOne",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrd... | 73 | [
"AbsoluteValue",
"AbsoluteValue.abs",
"AbsoluteValue.funLike",
"DFunLike.coe",
"DistribLattice.toLattice",
"Eq.refl",
"IsStrictOrderedRing",
"Lattice.toSemilatticeInf",
"LinearOrder",
"Ring",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"instDistribLatticeOfLinearOrder"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Euclidean | AbsoluteValue.abs_isEuclidean | AbsoluteValue | null | 32 | [
"AbsoluteValue.IsEuclidean",
"AbsoluteValue.abs",
"DistribLattice.toLattice",
"Int",
"Int.euclideanDomain",
"Int.instIsStrictOrderedRing",
"Int.instLinearOrder",
"Int.instRing",
"Lattice.toSemilatticeInf",
"Ring.toSemiring",
"SemilatticeInf.toPartialOrder",
"instDistribLatticeOfLinearOrder"
] | 155 | [
"AbsoluteValue.IsEuclidean.mk",
"AbsoluteValue.abs",
"DistribLattice.toLattice",
"Eq",
"Eq.mpr",
"Iff",
"Iff.rfl",
"Int",
"Int.abs_eq_natAbs",
"Int.euclideanDomain",
"Int.instAddGroup",
"Int.instIsStrictOrderedRing",
"Int.instLTInt",
"Int.instLinearOrder",
"Int.instRing",
"Int.natAbs",... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.addGroupSeminormClass | AbsoluteValue | null | 88 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddGroupSeminormClass",
"AddGroupWithOne.toAddGroup",
"CommRing",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"Distrib.toMul",
"IsOrderedRing",
"MulZeroClass.toZero",
"NoZeroDivisors",
"PartialOrder",
"Ring",
"Ring.toAddGroupWithOne",
... | 176 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.map_neg",
"AbsoluteValue.map_zero",
"AbsoluteValue.subadditiveHomClass",
"AddCommMagma.toAdd",
"AddCommMonoid.toAddCommSemigroup",
"AddCommSemigroup.toAddCommMagma",
"AddGroup.toSubNegMonoid",
"AddGroupSeminormClass.mk",
"AddGroupWithOne.t... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.add_le | AbsoluteValue | null | 94 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Distrib.toAdd",
"HAdd.hAdd",
"LE.le",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",
"instDistribOfSemiring",
"instHAdd"
] | 39 | [
"AbsoluteValue",
"AbsoluteValue.add_le'",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.add_le' | AbsoluteValue | null | 95 | [
"AbsoluteValue",
"AbsoluteValue.toMulHom",
"Distrib.toAdd",
"Distrib.toMul",
"HAdd.hAdd",
"LE.le",
"MulHom.toFun",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",
"instDistribOfSemiring",
"instHAdd"
] | 26 | [
"AbsoluteValue",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.apply_natAbs_eq | AbsoluteValue | null | 122 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddGroupWithOne.toAddMonoidWithOne",
"AddGroupWithOne.toIntCast",
"AddMonoidWithOne.toNatCast",
"CommRing",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Distrib.toMul",
"Eq",
"Int",
"Int.cast",
"Int.natAbs",
"IsOrderedR... | 447 | [
"AbsoluteValue",
"AbsoluteValue.addGroupSeminormClass",
"AbsoluteValue.funLike",
"AddGroup.toSubtractionMonoid",
"AddGroupSeminormClass.map_neg_eq_map",
"AddGroupWithOne.toAddGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"AddGroupWithOne.toIntCast",
"AddMonoidWithOne.toNatCast",
"CommRing",
"Com... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.apply_nat_le_self | AbsoluteValue | null | 102 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toNatCast",
"DFunLike.coe",
"IsDomain",
"IsOrderedRing",
"LE.le",
"Nat",
"Nat.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",... | 763 | [
"AbsoluteValue",
"AbsoluteValue.add_le",
"AbsoluteValue.funLike",
"AbsoluteValue.map_one",
"AbsoluteValue.map_zero",
"AddCommMonoid.toAddCommSemigroup",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoidWithOne.toAddMonoid",
"AddMonoidWi... |
null | true | false | abbrev | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.casesOn | AbsoluteValue | abbrev | 215 | [
"AbsoluteValue",
"AbsoluteValue.mk",
"Distrib.toAdd",
"Distrib.toMul",
"Eq",
"HAdd.hAdd",
"Iff",
"LE.le",
"MulHom",
"MulHom.toFun",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",
"Zero.toOfNat0",
"instDistribOfSemiring"... | 342 | [
"AbsoluteValue",
"AbsoluteValue.mk",
"AbsoluteValue.rec",
"Distrib.toAdd",
"Distrib.toMul",
"Eq",
"HAdd.hAdd",
"Iff",
"LE.le",
"MulHom",
"MulHom.toFun",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",
"Zero.toOfNat0",
... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.coe_mk | AbsoluteValue | null | 241 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.mk",
"DFunLike.coe",
"Distrib.toAdd",
"Distrib.toMul",
"Eq",
"HAdd.hAdd",
"Iff",
"LE.le",
"MulHom",
"MulHom.funLike",
"MulHom.toFun",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.... | 218 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.mk",
"DFunLike.coe",
"Distrib.toAdd",
"Distrib.toMul",
"Eq",
"HAdd.hAdd",
"Iff",
"LE.le",
"MulHom",
"MulHom.toFun",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semiring",... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.coe_toMonoidHom | AbsoluteValue | null | 100 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.toMonoidHom",
"DFunLike.coe",
"Eq",
"IsDomain",
"MonoidHom",
"MonoidHom.instFunLike",
"MulOneClass.toMulOne",
"MulZeroOneClass.toMulOneClass",
"Nontrivial",
"PartialOrder",
"Semiring",
"instMulZeroOneClassOfSemiring"
] | 83 | [
"AbsoluteValue",
"AbsoluteValue.toMonoidHom",
"DFunLike.coe",
"IsDomain",
"MonoidHom",
"MonoidHom.instFunLike",
"MulOneClass.toMulOne",
"MulZeroOneClass.toMulOneClass",
"Nontrivial",
"PartialOrder",
"Semiring",
"instMulZeroOneClassOfSemiring",
"rfl"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.coe_toMonoidWithZeroHom | AbsoluteValue | null | 88 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.toMonoidWithZeroHom",
"DFunLike.coe",
"Eq",
"IsDomain",
"MonoidWithZeroHom",
"MonoidWithZeroHom.funLike",
"Nontrivial",
"PartialOrder",
"Semiring",
"instMulZeroOneClassOfSemiring"
] | 71 | [
"AbsoluteValue",
"AbsoluteValue.toMonoidWithZeroHom",
"DFunLike.coe",
"IsDomain",
"MonoidWithZeroHom",
"MonoidWithZeroHom.funLike",
"Nontrivial",
"PartialOrder",
"Semiring",
"instMulZeroOneClassOfSemiring",
"rfl"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.coe_toMulHom | AbsoluteValue | null | 83 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.toMulHom",
"DFunLike.coe",
"Distrib.toMul",
"Eq",
"MulHom",
"MulHom.funLike",
"PartialOrder",
"Semiring",
"instDistribOfSemiring"
] | 66 | [
"AbsoluteValue",
"AbsoluteValue.toMulHom",
"DFunLike.coe",
"Distrib.toMul",
"MulHom",
"MulHom.funLike",
"PartialOrder",
"Semiring",
"instDistribOfSemiring",
"rfl"
] |
3 | false | false | definition | Mathlib.Topology.Algebra.Ring.Basic | AbsoluteValue.comp | AbsoluteValue | regular | 78 | [
"AbsoluteValue",
"DFunLike.coe",
"Function.Injective",
"PartialOrder",
"RingHom",
"RingHom.instFunLike",
"Semiring",
"Semiring.toNonAssocSemiring"
] | 180 | [
"AbsoluteValue",
"AbsoluteValue.comp._proof_1",
"AbsoluteValue.comp._proof_2",
"AbsoluteValue.comp._proof_3",
"AbsoluteValue.comp._proof_4",
"AbsoluteValue.mk",
"AbsoluteValue.toMulHom",
"DFunLike.coe",
"Distrib.toMul",
"Function.Injective",
"MulHom",
"MulHom.comp",
"MulHomClass.toMulHom",
... |
null | true | true | theorem | Mathlib.Topology.Algebra.Ring.Basic | AbsoluteValue.comp._proof_1 | AbsoluteValue.comp | null | 55 | [
"Distrib.toMul",
"MulHomClass",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toDistrib",
"RingHom",
"RingHom.instFunLike",
"Semiring",
"Semiring.toNonAssocSemiring"
] | 57 | [
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalRingHomClass.toMulHomClass",
"RingHom",
"RingHom.instFunLike",
"RingHom.instRingHomClass",
"RingHomClass.toNonUnitalRingHomClass",
"Semiring",
"Semiring.toNonAssocSemiring"
] |
null | true | true | theorem | Mathlib.Topology.Algebra.Ring.Basic | AbsoluteValue.comp._proof_2 | AbsoluteValue.comp | null | 150 | [
"AbsoluteValue",
"AbsoluteValue.comp._proof_1",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Distrib.toMul",
"LE.le",
"MulHom",
"MulHom.funLike",
"MulHomClass.toMulHom",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"RingHom.i... | 136 | [
"AbsoluteValue",
"AbsoluteValue.nonneg",
"DFunLike.coe",
"Distrib.toMul",
"MulHom",
"MulHom.funLike",
"MulHomClass.toMulHom",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalRingHomClass.toMulHomClass",
"PartialOrder",
"RingHom",
"RingHom.instFunLike",
"RingHom.instRingHomClass",
... |
null | true | true | theorem | Mathlib.Topology.Algebra.Ring.Basic | AbsoluteValue.comp._proof_3 | AbsoluteValue.comp | null | 188 | [
"AbsoluteValue",
"AbsoluteValue.comp._proof_1",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Distrib.toMul",
"Eq",
"Function.Injective",
"Iff",
"MulHom",
"MulHom.funLike",
"MulHomClass.toMulHom",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"RingHom",
"RingHom.instFunLike",
"Se... | 271 | [
"AbsoluteValue",
"AbsoluteValue.eq_zero",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Distrib.toMul",
"Eq",
"Function.Injective",
"Iff.trans",
"MonoidWithZeroHomClass.toZeroHomClass",
"MulHom",
"MulHom.funLike",
"MulHomClass.toMulHom",
"MulZeroClass.toZero",
"NonAssocSemiring.toMulZeroOneCla... |
null | true | true | theorem | Mathlib.Topology.Algebra.Ring.Basic | AbsoluteValue.comp._proof_4 | AbsoluteValue.comp | null | 199 | [
"AbsoluteValue",
"AbsoluteValue.comp._proof_1",
"AbsoluteValue.funLike",
"AbsoluteValue.toMulHom",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoid.toAddZeroClass",
"AddMonoidWithOne.toAddMonoid",
"AddZero.toAdd",
"AddZeroClass.toAddZero",
"DFunLike.coe",
"Distrib.toAdd",
"Distrib.toMul",... | 298 | [
"AbsoluteValue",
"AbsoluteValue.add_le",
"AbsoluteValue.funLike",
"AbsoluteValue.toMulHom",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoid.toAddZeroClass",
"AddMonoidHomClass.toAddHomClass",
"AddMonoidWithOne.toAddMonoid",
"AddZero.toAdd",
"AddZeroClass.toAddZero",
"DFunLike.coe",
"Dist... |
null | true | false | theorem | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | AbsoluteValue.comp.congr_simp | AbsoluteValue.comp | null | 177 | [
"AbsoluteValue",
"AbsoluteValue.comp",
"DFunLike.coe",
"Eq",
"Eq.ndrec",
"Function.Injective",
"PartialOrder",
"RingHom",
"RingHom.instFunLike",
"Semiring",
"Semiring.toNonAssocSemiring"
] | 280 | [
"AbsoluteValue",
"AbsoluteValue.comp",
"DFunLike.coe",
"Eq",
"Eq.ndrec",
"Eq.rec",
"Eq.refl",
"Function.Injective",
"PartialOrder",
"RingHom",
"RingHom.instFunLike",
"Semiring",
"Semiring.toNonAssocSemiring"
] |
1 | true | false | definition | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.ctorIdx | AbsoluteValue | regular | 26 | [
"AbsoluteValue",
"Nat",
"PartialOrder",
"Semiring"
] | 26 | [
"AbsoluteValue",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.denseRange_algebraMap_pi | AbsoluteValue | null | 206 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsNontrivial",
"Algebra.algebraMap",
"Algebra.id",
"CommSemiring.toSemiring",
"DFunLike.coe",
"DenseRange",
"DivisionSemiring.toSemiring",
"Field",
"Field.toSemifield",
"Finite",
"NormedCommRing.toSeminormedCommRing",
"NormedField.to... | 4,932 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv",
"AbsoluteValue.funLike",
"AbsoluteValue.monoidWithZeroHomClass",
"AbsoluteValue.nonpos_iff._simp_1",
"AbsoluteValue.pos_iff",
"AbsoluteValue.tendsto_div_one_add_pow_nhds_ze... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.eq_on_nat_iff_eq_on_int | AbsoluteValue | null | 143 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddGroupWithOne.toAddMonoidWithOne",
"AddGroupWithOne.toIntCast",
"AddMonoidWithOne.toNatCast",
"CommRing",
"CommRing.toCommSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"Distrib.toMul",
"Eq",
"Iff",
"Int",
"Int.cast",
"IsOrderedRing",
... | 594 | [
"AbsoluteValue",
"AbsoluteValue.addGroupSeminormClass",
"AbsoluteValue.funLike",
"AddGroup.toSubtractionMonoid",
"AddGroupSeminormClass.map_neg_eq_map",
"AddGroupWithOne.toAddGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"AddGroupWithOne.toIntCast",
"AddMonoidWithOne.toNatCast",
"CommRing",
"Com... |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.eq_zero | AbsoluteValue | null | 85 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Eq",
"Iff",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"Semiring",
"Zero.toOfNat0",
"instMulZeroClassOfSemiring"
] | 36 | [
"AbsoluteValue",
"AbsoluteValue.eq_zero'",
"PartialOrder",
"Semiring"
] |
null | false | false | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.eq_zero' | AbsoluteValue | null | 92 | [
"AbsoluteValue",
"AbsoluteValue.toMulHom",
"Distrib.toMul",
"Eq",
"Iff",
"MulHom.toFun",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"Semiring",
"Zero.toOfNat0",
"instDistribOfSemiring",
"instMulZeroClassOfSemiring"
] | 26 | [
"AbsoluteValue",
"PartialOrder",
"Semiring"
] |
null | true | true | theorem | Mathlib.Algebra.Order.AbsoluteValue.Basic | AbsoluteValue.eq_zero._simp_1 | AbsoluteValue.eq_zero | null | 87 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Eq",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"Semiring",
"Zero.toOfNat0",
"instMulZeroClassOfSemiring"
] | 94 | [
"AbsoluteValue",
"AbsoluteValue.eq_zero",
"AbsoluteValue.funLike",
"DFunLike.coe",
"Eq",
"MulZeroClass.toZero",
"OfNat.ofNat",
"PartialOrder",
"Semiring",
"Zero.toOfNat0",
"instMulZeroClassOfSemiring",
"propext"
] |
null | false | false | theorem | Mathlib.NumberTheory.Height.MvPolynomial | AbsoluteValue.eval_mvPolynomial_le | AbsoluteValue | null | 256 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.coeff",
"AddMonoidAlgebra.nonAssocSemiring",
"CommSemiring.toSemiring",
"DFunLike.coe",
"DivisionSemiring.toSemiring",
"Field",
"Field.toSemifield",
"Finite",
"Finsupp",
"Finsupp.instAddZeroClass",
"Fin... | 1,271 | [
"AbsoluteValue",
"AbsoluteValue.funLike",
"AbsoluteValue.map_mul",
"AbsoluteValue.map_pow",
"AbsoluteValue.map_prod",
"AbsoluteValue.nonnegHomClass",
"AbsoluteValue.sum_le",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.coeff",
"AddMonoidAlgebra.nonAssocSemiring",
"CommMonoid.toMonoid",
"CommR... |
null | false | false | theorem | Mathlib.Analysis.AbsoluteValue.Equivalence | AbsoluteValue.exists_lt_one_one_le_of_not_isEquiv | AbsoluteValue | null | 288 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"Archimedean",
"DFunLike.coe",
"Distrib.toAdd",
"DistribLattice.toLattice",
"DivisionSemiring.toSemiring",
"Exists",
... | 507 | [
"AbsoluteValue",
"AbsoluteValue.IsEquiv",
"AbsoluteValue.IsNontrivial",
"AbsoluteValue.funLike",
"AbsoluteValue.isEquiv_of_lt_one_imp",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And",
"Archimedean",
"DFunLike.coe",
"Distrib.toAdd",
"DistribLattice.toLattice",
"Div... |
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