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The dataset generation failed
Error code: DatasetGenerationError
Exception: ArrowNotImplementedError
Message: extension
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1893, in _prepare_split_single
writer.write_table(table)
File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 765, in write_table
self._write_table(pa_table, writer_batch_size=writer_batch_size)
File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 773, in _write_table
pa_table = table_cast(pa_table, self._schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2281, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2234, in cast_table_to_schema
table[name] if name in table_column_names else pa.array([None] * len(table), type=schema.field(name).type),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "pyarrow/array.pxi", line 375, in pyarrow.lib.array
File "pyarrow/array.pxi", line 46, in pyarrow.lib._sequence_to_array
File "pyarrow/error.pxi", line 155, in pyarrow.lib.pyarrow_internal_check_status
File "pyarrow/error.pxi", line 92, in pyarrow.lib.check_status
pyarrow.lib.ArrowNotImplementedError: extension
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1342, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 907, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1739, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1925, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
isProp bool | kind string | name list | typeFallback string | typeFull string | typeReadable string | typeReferences list | valueReferences list |
|---|---|---|---|---|---|---|---|
true | theorem | [
"\"AddConstMap\"",
"\"mkFract\"",
"\"_proof_2\""
] | forall {R : Type.{u_1}} {G : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.4 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.7 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.10 : IsStrictOrderedRing.{u_1} R (R... | ∀ {R : Type u_1} {G : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R]
[inst_3 : FloorRing R] [inst_4 : AddGroup G] (a : G) (x : ↑(Set.Ico 0 1) → G),
(fun f x => f ↑x) ((fun f => { toFun := fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a, map_add_const' := ⋯ }) x) = x | ∀ {R : Type u_1} {G : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R]
[inst_3 : FloorRing R] [inst_4 : AddGroup G] (a : G) (x : ↑(Set.Ico 0 1) → G),
(fun f x => f ↑x) ((fun f => { toFun := fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a, map_add_const' := ⋯ }) x) = x | [
[
"Ring",
"toNonAssocRing"
],
[
"PartialOrder",
"toPreorder"
],
[
"Membership",
"mem"
],
[
"Preorder",
"toLT"
],
[
"AddGroupWithOne",
"toAddMonoidWithOne"
],
[
"Subtype",
"val"
],
[
"Set",
"Elem"
],
[
"NonUnitalNonAssocRing",
... | [
[
"\"Int\"",
"\"instCommRing\""
],
[
"\"SubtractionMonoid\"",
"\"toSubNegZeroMonoid\""
],
[
"\"Ring\"",
"\"toNonAssocRing\""
],
[
"\"PartialOrder\"",
"\"toPreorder\""
],
[
"\"Eq\"",
"\"trans\""
],
[
"\"Membership\"",
"\"mem\""
],
[
"\"Preor... |
false | definition | [
"\"AddConstMap\"",
"\"ctorIdx\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} {inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.4 : Add.{u_1} G} {inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.7 : Add.{u_2} H} {a : G} {b : H}, (AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.... | {G : Type u_1} → {H : Type u_2} → {inst : Add G} → {inst_1 : Add H} → {a : G} → {b : H} → AddConstMap G H a b → ℕ | {G : Type u_1} → {H : Type u_2} → {inst : Add G} → {inst_1 : Add H} → {a : G} → {b : H} → AddConstMap G H a b → ℕ | [
[
"Nat"
],
[
"AddConstMap"
],
[
"Add"
]
] | [] |
true | theorem | [
"\"AddConstMap\"",
"\"mk\"",
"\"inj\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} {inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.4 : Add.{u_1} G} {inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.7 : Add.{u_2} H} {a : G} {b : H} {toFun : G -> H} {map_add_const' : forall (x : G), Eq.{succ u_2} H (toFun (HAdd.hAdd.{u_1, u_1,... | ∀ {G : Type u_1} {H : Type u_2} {inst : Add G} {inst_1 : Add H} {a : G} {b : H} {toFun : G → H}
{map_add_const' : ∀ (x : G), toFun (x + a) = toFun x + b} {toFun_1 : G → H}
{map_add_const'_1 : ∀ (x : G), toFun_1 (x + a) = toFun_1 x + b},
{ toFun := toFun, map_add_const' := map_add_const' } = { toFun := toFun_1, ma... | ∀ {G : Type u_1} {H : Type u_2} {inst : Add G} {inst_1 : Add H} {a : G} {b : H} {toFun : G → H}
{map_add_const' : ∀ (x : G), toFun (x + a) = toFun x + b} {toFun_1 : G → H}
{map_add_const'_1 : ∀ (x : G), toFun_1 (x + a) = toFun_1 x + b},
{ toFun := toFun, map_add_const' := map_add_const' } = { toFun := toFun_1, ma... | [
[
"HAdd",
"hAdd"
],
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"instHAdd"
],
[
"Add"
],
[
"Eq"
]
] | [
[
"\"eq_of_heq\""
],
[
"\"Eq\""
],
[
"\"AddConstMap\"",
"\"mk\"",
"\"noConfusion\""
]
] |
false | definition | [
"\"AddConstMap\"",
"\"instFunLike\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3951779108._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3951779108._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H}, FunLike.{max (succ u_2) (succ u_1), succ u_1, succ u_2} (AddConstMap.{u_1, u_2} G H inst._@.Ma... | {G : Type u_1} →
{H : Type u_2} → [inst : Add G] → [inst_1 : Add H] → {a : G} → {b : H} → FunLike (AddConstMap G H a b) G H | {G : Type u_1} →
{H : Type u_2} → [inst : Add G] → [inst_1 : Add H] → {a : G} → {b : H} → FunLike (AddConstMap G H a b) G H | [
[
"FunLike"
],
[
"AddConstMap"
],
[
"Add"
]
] | [
[
"\"DFunLike\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"toFun\""
],
[
"\"AddConstMap\"",
"\"instFunLike\"",
"\"_proof_1\""
]
] |
false | definition | [
"\"AddConstMap\"",
"\"instVAddOfVAddAssocClass\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.544706179._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.544706179._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} {K : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.544706179._hygCtx._hyg.13 : VAdd.{u_3... | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} → {b : H} → {K : Type u_3} → [inst_2 : VAdd K H] → [VAddAssocClass K H H] → VAdd K (AddConstMap G H a b) | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} → {b : H} → {K : Type u_3} → [inst_2 : VAdd K H] → [VAddAssocClass K H H] → VAdd K (AddConstMap G H a b) | [
[
"VAdd"
],
[
"AddConstMap"
],
[
"Add"
],
[
"Add",
"toVAdd"
],
[
"VAddAssocClass"
]
] | [
[
"\"instHVAdd\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"instVAddOfVAddAssocClass\"",
"\"_proof_1\""
],
[
"\"Function\"",
"\"hasVAdd\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"in... |
false | definition | [
"\"AddConstMap\"",
"\"instMul\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3379617806._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, Mul.{u_1} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.3379617806._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.3379617806._hygCtx._hyg.4 a a) | {G : Type u_1} → [inst : Add G] → {a : G} → Mul (AddConstMap G G a a) | {G : Type u_1} → [inst : Add G] → {a : G} → Mul (AddConstMap G G a a) | [
[
"AddConstMap"
],
[
"Add"
],
[
"Mul"
]
] | [
[
"\"Mul\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"comp\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_add_nsmul\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.508567400._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {a : G} {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.508567400._hygCtx._hyg.12 : AddMonoid.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Bas... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddMonoid G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H a b] (f : F) (x : G) (n : ℕ), f (x + n • a) = f x + n • b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddMonoid G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H a b] (f : F) (x : G) (n : ℕ), f (x + n • a) = f x + n • b | [
[
"FunLike"
],
[
"instHAdd"
],
[
"AddMonoid"
],
[
"AddConstMapClass"
],
[
"DFunLike",
"coe"
],
[
"HAdd",
"hAdd"
],
[
"Nat"
],
[
"AddMonoid",
"toNSMul"
],
[
"AddMonoid",
"toAddSemigroup"
],
[
"HSMul",
"hSMul"
],
[
... | [
[
"\"Function\"",
"\"Semiconj\"",
"\"iterate_right\""
],
[
"\"Eq\"",
"\"mp\""
],
[
"\"instHAdd\""
],
[
"\"AddConstMapClass\"",
"\"semiconj\""
],
[
"\"add_right_iterate\""
],
[
"\"AddZero\"",
"\"toAdd\""
],
[
"\"AddZeroClass\"",
"\"toAddZero... |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_sub_int\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3830736427._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3830736427._hygCtx._hyg.12 : AddGroupWithOne.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.38307... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] [inst_1 : AddGroupWithOne G]
[inst_2 : AddGroupWithOne H] [AddConstMapClass F G H 1 1] (f : F) (x : G) (n : ℤ), f (x - ↑n) = f x - ↑n | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] [inst_1 : AddGroupWithOne G]
[inst_2 : AddGroupWithOne H] [AddConstMapClass F G H 1 1] (f : F) (x : G) (n : ℤ), f (x - ↑n) = f x - ↑n | [
[
"FunLike"
],
[
"AddGroupWithOne",
"toAddMonoidWithOne"
],
[
"AddGroupWithOne"
],
[
"AddConstMapClass"
],
[
"AddMonoidWithOne",
"toAddMonoid"
],
[
"Int",
"cast"
],
[
"DFunLike",
"coe"
],
[
"OfNat",
"ofNat"
],
[
"Int"
],
[
... | [
[
"\"Eq\"",
"\"trans\""
],
[
"\"AddGroupWithOne\"",
"\"toAddMonoidWithOne\""
],
[
"\"Int\"",
"\"cast\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"congrArg\""
],
[
"\"AddConstMapClass\"",
"\"map_sub_int'\""
],
[
"\"zsmul_one\""
],
[
"\"SubN... |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_add_one\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.4109334818._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.4109334818._hygCtx._hyg.12 : AddMonoidWithOne.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Ba... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddMonoidWithOne G]
[inst_2 : Add H] [AddConstMapClass F G H 1 b] (f : F) (x : G), f (x + 1) = f x + b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddMonoidWithOne G]
[inst_2 : Add H] [AddConstMapClass F G H 1 b] (f : F) (x : G), f (x + 1) = f x + b | [
[
"FunLike"
],
[
"instHAdd"
],
[
"Add"
],
[
"AddConstMapClass"
],
[
"AddMonoidWithOne",
"toAddMonoid"
],
[
"DFunLike",
"coe"
],
[
"OfNat",
"ofNat"
],
[
"HAdd",
"hAdd"
],
[
"One",
"toOfNat1"
],
[
"AddMonoid",
"toAddSe... | [
[
"\"AddConstMapClass\"",
"\"map_add_const\""
],
[
"\"One\"",
"\"toOfNat1\""
],
[
"\"AddMonoid\"",
"\"toAddSemigroup\""
],
[
"\"AddMonoidWithOne\"",
"\"toOne\""
],
[
"\"AddMonoidWithOne\"",
"\"toAddMonoid\""
],
[
"\"OfNat\"",
"\"ofNat\""
],
[
... |
true | theorem | [
"\"AddConstMap\"",
"\"instVAddOfVAddAssocClass\"",
"\"_proof_1\""
] | forall {G : Type.{u_3}} {H : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.544706179._hygCtx._hyg.4 : Add.{u_3} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.544706179._hygCtx._hyg.7 : Add.{u_1} H] {a : G} {b : H} {K : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.544706179._hygCtx._hyg.13 : VAdd.{u_2... | ∀ {G : Type u_3} {H : Type u_1} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} {K : Type u_2} [inst_2 : VAdd K H]
[VAddAssocClass K H H] (c : K) (f : AddConstMap G H a b) (x : G), (c +ᵥ ⇑f) (x + a) = (c +ᵥ ⇑f) x + b | ∀ {G : Type u_3} {H : Type u_1} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} {K : Type u_2} [inst_2 : VAdd K H]
[VAddAssocClass K H H] (c : K) (f : AddConstMap G H a b) (x : G), (c +ᵥ ⇑f) (x + a) = (c +ᵥ ⇑f) x + b | [
[
"VAdd"
],
[
"AddConstMap"
],
[
"instHVAdd"
],
[
"Add"
],
[
"instHAdd"
],
[
"Function",
"hasVAdd"
],
[
"DFunLike",
"coe"
],
[
"HVAdd",
"hVAdd"
],
[
"AddConstMap",
"instFunLike"
],
[
"VAddAssocClass"
],
[
"HAdd",
... | [
[
"\"AddConstMapClass\"",
"\"map_add_const\""
],
[
"\"instHVAdd\""
],
[
"\"AddConstMap\""
],
[
"\"Eq\"",
"\"trans\""
],
[
"\"True\""
],
[
"\"instHAdd\""
],
[
"\"outParam\""
],
[
"\"vadd_add_assoc\""
],
[
"\"Function\"",
"\"hasVAdd\""
... |
true | theorem | [
"\"AddConstMap\"",
"\"instMonoid\"",
"\"_proof_4\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 : Add.{u_1} G] {a : G} (x._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.38 : AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basi... | ∀ {G : Type u_1} [inst : Add G] {a : G} (x : AddConstMap G G a a) (x_1 : ℕ), ⇑(x ^ x_1) = ⇑(x ^ x_1) | ∀ {G : Type u_1} [inst : Add G] {a : G} (x : AddConstMap G G a a) (x_1 : ℕ), ⇑(x ^ x_1) = ⇑(x ^ x_1) | [
[
"instHPow"
],
[
"Nat"
],
[
"AddConstMap"
],
[
"Add"
],
[
"AddConstMap",
"instPowNat"
],
[
"Function",
"End"
],
[
"HPow",
"hPow"
],
[
"Eq"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
]
] | [
[
"\"instHPow\""
],
[
"\"rfl\""
],
[
"\"Nat\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"instPowNat\""
],
[
"\"Function\"",
"\"End\""
],
[
"\"HPow\"",
"\"hPow\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"... |
false | definition | [
"\"AddConstMap\"",
"\"id\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1952539257._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.1952539257._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.1952539257._hygCtx._hyg.4 a a | {G : Type u_1} → [inst : Add G] → {a : G} → AddConstMap G G a a | {G : Type u_1} → [inst : Add G] → {a : G} → AddConstMap G G a a | [
[
"AddConstMap"
],
[
"Add"
]
] | [
[
"\"AddConstMap\"",
"\"id\"",
"\"_proof_1\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"id\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_sub_one\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2894099257._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2894099257._hygCtx._hyg.12 : AddGroup.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2894... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddGroup G] [inst_2 : One G]
[inst_3 : AddGroup H] [AddConstMapClass F G H 1 b] (f : F) (x : G), f (x - 1) = f x - b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddGroup G] [inst_2 : One G]
[inst_3 : AddGroup H] [AddConstMapClass F G H 1 b] (f : F) (x : G), f (x - 1) = f x - b | [
[
"FunLike"
],
[
"AddConstMapClass"
],
[
"DFunLike",
"coe"
],
[
"OfNat",
"ofNat"
],
[
"SubNegMonoid",
"toAddMonoid"
],
[
"One",
"toOfNat1"
],
[
"SubNegMonoid",
"toSub"
],
[
"AddMonoid",
"toAddSemigroup"
],
[
"One"
],
[
... | [
[
"\"One\"",
"\"toOfNat1\""
],
[
"\"AddConstMapClass\"",
"\"map_sub_const\""
],
[
"\"OfNat\"",
"\"ofNat\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_sub_nsmul\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3544906112._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {a : G} {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3544906112._hygCtx._hyg.12 : AddGroup.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Ba... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddGroup G]
[inst_2 : AddGroup H] [AddConstMapClass F G H a b] (f : F) (x : G) (n : ℕ), f (x - n • a) = f x - n • b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddGroup G]
[inst_2 : AddGroup H] [AddConstMapClass F G H a b] (f : F) (x : G) (n : ℕ), f (x - n • a) = f x - n • b | [
[
"FunLike"
],
[
"AddConstMapClass"
],
[
"DFunLike",
"coe"
],
[
"Nat"
],
[
"AddMonoid",
"toNSMul"
],
[
"SubNegMonoid",
"toAddMonoid"
],
[
"AddMonoid",
"toAddSemigroup"
],
[
"SubNegMonoid",
"toSub"
],
[
"HSMul",
"hSMul"
],
... | [
[
"\"Eq\"",
"\"trans\""
],
[
"\"sub_add_cancel\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"congrArg\""
],
[
"\"SubNegMonoid\"",
"\"toSub\""
],
[
"\"AddConstMapClass\"",
"\"map_add_nsmul\""
],
[
"\"HSub\"",
"\"hSub\""
],
[
"\"Eq\"",
"\... |
true | theorem | [
"\"AddConstMap\"",
"\"one_def\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1818061511._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, Eq.{succ u_1} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.1818061511._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.1818061511._hygCtx._hyg.4 a a) (OfNat.ofNat.{u_1} (... | ∀ {G : Type u_1} [inst : Add G] {a : G}, 1 = AddConstMap.id | ∀ {G : Type u_1} [inst : Add G] {a : G}, 1 = AddConstMap.id | [
[
"One",
"toOfNat1"
],
[
"AddConstMap"
],
[
"Add"
],
[
"AddConstMap",
"instOne"
],
[
"Eq"
],
[
"AddConstMap",
"id"
],
[
"OfNat",
"ofNat"
]
] | [
[
"\"rfl\""
],
[
"\"One\"",
"\"toOfNat1\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"instOne\""
],
[
"\"OfNat\"",
"\"ofNat\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"instMonoid\"",
"\"_proof_3\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 : Add.{u_1} G] {a : G} (x._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.31 : AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basi... | ∀ {G : Type u_1} [inst : Add G] {a : G} (x x_1 : AddConstMap G G a a), ⇑(x * x_1) = ⇑(x * x_1) | ∀ {G : Type u_1} [inst : Add G] {a : G} (x x_1 : AddConstMap G G a a), ⇑(x * x_1) = ⇑(x * x_1) | [
[
"AddConstMap"
],
[
"Add"
],
[
"instHMul"
],
[
"HMul",
"hMul"
],
[
"AddConstMap",
"instMul"
],
[
"Function",
"End"
],
[
"Eq"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
]
] | [
[
"\"rfl\""
],
[
"\"AddConstMap\""
],
[
"\"instHMul\""
],
[
"\"HMul\"",
"\"hMul\""
],
[
"\"AddConstMap\"",
"\"instMul\""
],
[
"\"Function\"",
"\"End\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
]
] |
false | definition | [
"\"AddConstMap\"",
"\"toEnd\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, MonoidHom.{u_1, u_1} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 a a) (Function.End.{u... | {G : Type u_1} → [inst : Add G] → {a : G} → AddConstMap G G a a →* Function.End G | {G : Type u_1} → [inst : Add G] → {a : G} → AddConstMap G G a a →* Function.End G | [
[
"MulOneClass",
"toMulOne"
],
[
"AddConstMap",
"instMonoid"
],
[
"AddConstMap"
],
[
"Add"
],
[
"Monoid",
"toMulOneClass"
],
[
"MonoidHom"
],
[
"Function",
"End"
],
[
"instMonoidEnd"
]
] | [
[
"\"MulOneClass\"",
"\"toMulOne\""
],
[
"\"MonoidHom\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"MulOne\"",
"\"toOne\""
],
[
"\"AddConstMap\"",
"\"toEnd\"",
"\"_proof_2\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instF... |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_nsmul_add\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.4235594345._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {a : G} {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.4235594345._hygCtx._hyg.12 : AddCommMonoid.{u_2} G] [inst._@.Mathlib.Algebra.AddConstM... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddCommMonoid G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H a b] (f : F) (n : ℕ) (x : G), f (n • a + x) = f x + n • b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddCommMonoid G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H a b] (f : F) (n : ℕ) (x : G), f (n • a + x) = f x + n • b | [
[
"FunLike"
],
[
"instHAdd"
],
[
"AddMonoid"
],
[
"AddCommMonoid",
"toAddMonoid"
],
[
"AddConstMapClass"
],
[
"DFunLike",
"coe"
],
[
"HAdd",
"hAdd"
],
[
"AddCommMonoid"
],
[
"Nat"
],
[
"AddMonoid",
"toNSMul"
],
[
"Ad... | [
[
"\"instHAdd\""
],
[
"\"AddCommMonoid\"",
"\"toAddMonoid\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"congrArg\""
],
[
"\"HAdd\"",
"\"hAdd\""
],
[
"\"Nat\""
],
[
"\"AddCommMonoid\"",
"\"toAddCommSemigroup\""
],
[
"\"AddMonoid\"",
"\"toNSM... |
false | definition | [
"\"AddConstMap\"",
"\"instMonoid\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, Monoid.{u_1} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.3319175497._hygCtx._hyg.4 a a) | {G : Type u_1} → [inst : Add G] → {a : G} → Monoid (AddConstMap G G a a) | {G : Type u_1} → [inst : Add G] → {a : G} → Monoid (AddConstMap G G a a) | [
[
"AddConstMap"
],
[
"Add"
],
[
"Monoid"
]
] | [
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"instMonoid\"",
"\"_proof_2\""
],
[
"\"AddConstMap\"",
"\"instPowNat\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instMonoid\"",
"\"_proof_3\""
],
[
"\"AddConstMap\"",
"\"instFunLike... |
false | definition | [
"\"AddConstMap\"",
"\"recOn\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} {motive : (AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hyg... | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} →
{b : H} →
{motive : AddConstMap G H a b → Sort u} →
(t : AddConstMap G H a b) →
((toFun : G → H) →
(map_add_const' : ∀ (x : G), toFun (x + a) = toFu... | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} →
{b : H} →
{motive : AddConstMap G H a b → Sort u} →
(t : AddConstMap G H a b) →
((toFun : G → H) →
(map_add_const' : ∀ (x : G), toFun (x + a) = toFu... | [
[
"HAdd",
"hAdd"
],
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"instHAdd"
],
[
"Add"
],
[
"Eq"
]
] | [
[
"\"AddConstMap\"",
"\"rec\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"instAddConstMapClass\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1678344019._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.1678344019._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H}, AddConstMapClass.{max u_2 u_1, u_1, u_2} (AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.A... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H},
AddConstMapClass (AddConstMap G H a b) G H a b | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H},
AddConstMapClass (AddConstMap G H a b) G H a b | [
[
"AddConstMap"
],
[
"Add"
],
[
"AddConstMapClass"
],
[
"AddConstMap",
"instFunLike"
]
] | [
[
"\"AddConstMapClass\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"map_add_const'\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_one\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1966676765._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1966676765._hygCtx._hyg.12 : AddZeroClass.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddZeroClass G] [inst_2 : One G]
[inst_3 : Add H] [AddConstMapClass F G H 1 b] (f : F), f 1 = f 0 + b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddZeroClass G] [inst_2 : One G]
[inst_3 : Add H] [AddConstMapClass F G H 1 b] (f : F), f 1 = f 0 + b | [
[
"FunLike"
],
[
"AddZeroClass"
],
[
"Add"
],
[
"instHAdd"
],
[
"AddConstMapClass"
],
[
"AddZero",
"toAdd"
],
[
"AddZeroClass",
"toAddZero"
],
[
"DFunLike",
"coe"
],
[
"OfNat",
"ofNat"
],
[
"HAdd",
"hAdd"
],
[
"O... | [
[
"\"AddConstMapClass\"",
"\"map_const\""
],
[
"\"One\"",
"\"toOfNat1\""
],
[
"\"OfNat\"",
"\"ofNat\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"toEnd_apply\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, Eq.{succ u_1} ((AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 a a) -> G -> G) (DFunLike.c... | ∀ {G : Type u_1} [inst : Add G] {a : G}, ⇑AddConstMap.toEnd = DFunLike.coe | ∀ {G : Type u_1} [inst : Add G] {a : G}, ⇑AddConstMap.toEnd = DFunLike.coe | [
[
"MulOneClass",
"toMulOne"
],
[
"AddConstMap"
],
[
"Add"
],
[
"MonoidHom"
],
[
"AddConstMap",
"toEnd"
],
[
"MonoidHom",
"instFunLike"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
],
[
"AddConstMap",
"instMonoid"... | [
[
"\"MulOneClass\"",
"\"toMulOne\""
],
[
"\"AddConstMap\"",
"\"instMonoid\""
],
[
"\"AddConstMap\""
],
[
"\"Eq\"",
"\"refl\""
],
[
"\"AddConstMap\"",
"\"toEnd\""
],
[
"\"Monoid\"",
"\"toMulOneClass\""
],
[
"\"MonoidHom\""
],
[
"\"Monoid... |
true | theorem | [
"\"AddConstMap\"",
"\"instAddActionOfVAddAssocClass\"",
"\"_proof_1\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1933080343._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.1933080343._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H}, Function.Injective.{succ (max u_1 u_2), max (succ u_1) (succ u_2)} (AddConstMap.{u_1, u_2} G H... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H}, Function.Injective fun f => ⇑f | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H}, Function.Injective fun f => ⇑f | [
[
"AddConstMap"
],
[
"Add"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
],
[
"Function",
"Injective"
]
] | [
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
],
[
"\"DFunLike\"",
"\"coe_injective\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"coe_addLeftHom_apply\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1543760281._hygCtx._hyg.3 : AddMonoid.{u_1} G] {a : G} (c : Multiplicative.{u_1} G), Eq.{succ u_1} (G -> G) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (AddConstMap.{u_1, u_1} G G (AddSemigroup.toAdd.{u_1} G (AddMonoid.toAddSemigroup.{u_1} G inst._@.Ma... | ∀ {G : Type u_1} [inst : AddMonoid G] {a : G} (c : Multiplicative G),
⇑(AddConstMap.addLeftHom c) = Multiplicative.toAdd c +ᵥ id | ∀ {G : Type u_1} [inst : AddMonoid G] {a : G} (c : Multiplicative G),
⇑(AddConstMap.addLeftHom c) = Multiplicative.toAdd c +ᵥ id | [
[
"MulOneClass",
"toMulOne"
],
[
"Multiplicative",
"toAdd"
],
[
"Equiv",
"instEquivLike"
],
[
"MonoidHom"
],
[
"MonoidHom",
"instFunLike"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
],
[
"Equiv"
],
[
"AddAction"... | [
[
"\"MulOneClass\"",
"\"toMulOne\""
],
[
"\"AddConstMap\""
],
[
"\"MonoidHom\""
],
[
"\"MonoidHom\"",
"\"instFunLike\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
],
[
"\"AddConstMap\"",
"\"addLeftHom\""
],
[
... |
false | definition | [
"\"AddConstMap\"",
"\"instOne\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3497455563._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, One.{u_1} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.3497455563._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.3497455563._hygCtx._hyg.4 a a) | {G : Type u_1} → [inst : Add G] → {a : G} → One (AddConstMap G G a a) | {G : Type u_1} → [inst : Add G] → {a : G} → One (AddConstMap G G a a) | [
[
"AddConstMap"
],
[
"Add"
],
[
"One"
]
] | [
[
"\"AddConstMap\""
],
[
"\"One\"",
"\"mk\""
],
[
"\"AddConstMap\"",
"\"id\""
]
] |
false | definition | [
"\"AddConstMap\"",
"\"casesOn\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} {motive : (AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hyg... | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} →
{b : H} →
{motive : AddConstMap G H a b → Sort u} →
(t : AddConstMap G H a b) →
((toFun : G → H) →
(map_add_const' : ∀ (x : G), toFun (x + a) = toFu... | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} →
{b : H} →
{motive : AddConstMap G H a b → Sort u} →
(t : AddConstMap G H a b) →
((toFun : G → H) →
(map_add_const' : ∀ (x : G), toFun (x + a) = toFu... | [
[
"HAdd",
"hAdd"
],
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"instHAdd"
],
[
"Add"
],
[
"Eq"
]
] | [
[
"\"AddConstMap\"",
"\"rec\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"monotone_iff_Icc\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.585965779._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {a : G} {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.585965779._hygCtx._hyg.12 : AddCommGroup.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddCommGroup G]
[inst_2 : LinearOrder G] [IsOrderedAddMonoid G] [Archimedean G] [inst_5 : AddCommGroup H] [inst_6 : PartialOrder H]
[IsOrderedAddMonoid H] [AddConstMapClass F G H a b] {f : F},
0 < a → ∀ (l : G), Monoto... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddCommGroup G]
[inst_2 : LinearOrder G] [IsOrderedAddMonoid G] [Archimedean G] [inst_5 : AddCommGroup H] [inst_6 : PartialOrder H]
[IsOrderedAddMonoid H] [AddConstMapClass F G H a b] {f : F},
0 < a → ∀ (l : G), Monoto... | [
[
"SubtractionMonoid",
"toSubNegZeroMonoid"
],
[
"PartialOrder",
"toPreorder"
],
[
"Set",
"Icc"
],
[
"Preorder",
"toLT"
],
[
"SubtractionCommMonoid",
"toSubtractionMonoid"
],
[
"DFunLike",
"coe"
],
[
"SubNegZeroMonoid",
"toNegZeroClass"... | [
[
"\"PartialOrder\"",
"\"toPreorder\""
],
[
"\"Set\"",
"\"Icc\""
],
[
"\"AddCommGroup\"",
"\"toAddGroup\""
],
[
"\"Preorder\"",
"\"toLT\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"Iff\"",
"\"intro\""
],
[
"\"instDistribLatticeOfLinearOrder\""... |
true | theorem | [
"\"AddConstMap\"",
"\"coe_vadd\"",
"\"_simp_1\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.50153765._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.50153765._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} {K : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.50153765._hygCtx._hyg.13 : VAdd.{u_3, u... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} {K : Type u_3} [inst_2 : VAdd K H]
[inst_3 : VAddAssocClass K H H] (c : K) (f : AddConstMap G H a b), c +ᵥ ⇑f = ⇑(c +ᵥ f) | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} {K : Type u_3} [inst_2 : VAdd K H]
[inst_3 : VAddAssocClass K H H] (c : K) (f : AddConstMap G H a b), c +ᵥ ⇑f = ⇑(c +ᵥ f) | [
[
"VAdd"
],
[
"instHVAdd"
],
[
"AddConstMap"
],
[
"Add"
],
[
"Add",
"toVAdd"
],
[
"AddConstMap",
"instVAddOfVAddAssocClass"
],
[
"Function",
"hasVAdd"
],
[
"Eq"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
... | [
[
"\"instHVAdd\""
],
[
"\"AddConstMap\""
],
[
"\"Eq\"",
"\"symm\""
],
[
"\"AddConstMap\"",
"\"coe_vadd\""
],
[
"\"Function\"",
"\"hasVAdd\""
],
[
"\"AddConstMap\"",
"\"instVAddOfVAddAssocClass\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"H... |
true | theorem | [
"\"AddConstMap\"",
"\"toEnd\"",
"\"_proof_2\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 : Add.{u_1} G] {a : G} (x._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.37 : AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.880101153._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.8... | ∀ {G : Type u_1} [inst : Add G] {a : G} (x x_1 : AddConstMap G G a a), ⇑(x * x_1) = ⇑(x * x_1) | ∀ {G : Type u_1} [inst : Add G] {a : G} (x x_1 : AddConstMap G G a a), ⇑(x * x_1) = ⇑(x * x_1) | [
[
"MulOneClass",
"toMulOne"
],
[
"MulOne",
"toMul"
],
[
"AddConstMap",
"instMonoid"
],
[
"AddConstMap"
],
[
"Add"
],
[
"Monoid",
"toMulOneClass"
],
[
"instHMul"
],
[
"HMul",
"hMul"
],
[
"Function",
"End"
],
[
"Eq"
... | [
[
"\"MulOneClass\"",
"\"toMulOne\""
],
[
"\"rfl\""
],
[
"\"MulOne\"",
"\"toMul\""
],
[
"\"AddConstMap\"",
"\"instMonoid\""
],
[
"\"AddConstMap\""
],
[
"\"Monoid\"",
"\"toMulOneClass\""
],
[
"\"instHMul\""
],
[
"\"HMul\"",
"\"hMul\""
]... |
false | definition | [
"\"AddConstMap\"",
"\"replaceConsts\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2065987452._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2065987452._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H}, (AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.AddConstMap.Basic.2065987452._hygCtx._hyg.... | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} → {b : H} → AddConstMap G H a b → (a' : G) → (b' : H) → a = a' → b = b' → AddConstMap G H a' b' | {G : Type u_1} →
{H : Type u_2} →
[inst : Add G] →
[inst_1 : Add H] →
{a : G} → {b : H} → AddConstMap G H a b → (a' : G) → (b' : H) → a = a' → b = b' → AddConstMap G H a' b' | [
[
"AddConstMap"
],
[
"Add"
],
[
"Eq"
]
] | [
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"AddConstMap\"",
"\"replaceConsts\"",
"\"_proof_1\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"addLeftHom\"",
"\"_proof_2\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1543760281._hygCtx._hyg.3 : AddMonoid.{u_1} G] {a : G} (x._@.Mathlib.Algebra.AddConstMap.Basic.1543760281._hygCtx._hyg.42 : Multiplicative.{u_1} G) (x._@.Mathlib.Algebra.AddConstMap.Basic.1543760281._hygCtx._hyg.44 : Multiplicative.{u_1} G), Eq.{succ u_... | ∀ {G : Type u_1} [inst : AddMonoid G] {a : G} (x x_1 : Multiplicative G),
Multiplicative.toAdd (x * x_1) +ᵥ AddConstMap.id =
(Multiplicative.toAdd x +ᵥ AddConstMap.id) * (Multiplicative.toAdd x_1 +ᵥ AddConstMap.id) | ∀ {G : Type u_1} [inst : AddMonoid G] {a : G} (x x_1 : Multiplicative G),
Multiplicative.toAdd (x * x_1) +ᵥ AddConstMap.id =
(Multiplicative.toAdd x +ᵥ AddConstMap.id) * (Multiplicative.toAdd x_1 +ᵥ AddConstMap.id) | [
[
"MulOneClass",
"toMulOne"
],
[
"Multiplicative",
"toAdd"
],
[
"Equiv",
"instEquivLike"
],
[
"HMul",
"hMul"
],
[
"DFunLike",
"coe"
],
[
"Equiv"
],
[
"AddConstMap",
"id"
],
[
"AddAction",
"toAddSemigroupAction"
],
[
"Mul... | [
[
"\"MulOneClass\"",
"\"toMulOne\""
],
[
"\"Multiplicative\"",
"\"toAdd\""
],
[
"\"Equiv\"",
"\"instEquivLike\""
],
[
"\"HMul\"",
"\"hMul\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
],
[
"\"Equiv\""
],
[
... |
true | theorem | [
"\"_private\"",
"\"Mathlib\"",
"\"Algebra\"",
"\"AddConstMap\"",
"\"Basic\"",
"0",
"\"AddConstMapClass\"",
"\"map_add_nat'\"",
"\"_simp_1_1\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.508567400._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {a : G} {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.508567400._hygCtx._hyg.12 : AddMonoid.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Bas... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddMonoid G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H a b] (f : F) (x : G) (n : ℕ), f x + n • b = f (x + n • a) | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} {b : H} [inst_1 : AddMonoid G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H a b] (f : F) (x : G) (n : ℕ), f x + n • b = f (x + n • a) | [
[
"FunLike"
],
[
"instHAdd"
],
[
"AddMonoid"
],
[
"AddConstMapClass"
],
[
"DFunLike",
"coe"
],
[
"HAdd",
"hAdd"
],
[
"Nat"
],
[
"AddMonoid",
"toNSMul"
],
[
"AddMonoid",
"toAddSemigroup"
],
[
"HSMul",
"hSMul"
],
[
... | [
[
"\"HAdd\"",
"\"hAdd\""
],
[
"\"Nat\""
],
[
"\"AddMonoid\"",
"\"toNSMul\""
],
[
"\"instHAdd\""
],
[
"\"AddMonoid\"",
"\"toAddSemigroup\""
],
[
"\"AddConstMapClass\"",
"\"map_add_nsmul\""
],
[
"\"HSMul\"",
"\"hSMul\""
],
[
"\"Eq\"",
... |
false | definition | [
"\"AddConstMap\"",
"\"_aux_Mathlib_Algebra_AddConstMap_Basic___unexpand_AddConstMap_1\""
] | Lean.PrettyPrinter.Unexpander | Lean.PrettyPrinter.Unexpander | Lean.PrettyPrinter.Unexpander | [
[
"Lean",
"PrettyPrinter",
"Unexpander"
]
] | [
[
"\"Lean\"",
"\"Name\""
],
[
"\"Lean\"",
"\"TSyntax\"",
"\"raw\""
],
[
"\"Bool\"",
"false"
],
[
"\"Lean\"",
"\"MonadQuotation\"",
"\"getCurrMacroScope\""
],
[
"\"Lean\"",
"\"MacroScope\""
],
[
"\"Lean\"",
"\"SourceInfo\""
],
[
"\"L... |
true | theorem | [
"\"AddConstMap\"",
"\"mkFract\"",
"\"_proof_4\""
] | forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.4 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.7 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.10 : IsStrictOrderedRing.{u_1} R (Ring.toSemiring.{u... | ∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [inst_3 : FloorRing R] (x : R),
0 ≤ Int.fract x ∧ Int.fract x < 1 | ∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [inst_3 : FloorRing R] (x : R),
0 ≤ Int.fract x ∧ Int.fract x < 1 | [
[
"PartialOrder",
"toPreorder"
],
[
"Ring",
"toNonAssocRing"
],
[
"Preorder",
"toLT"
],
[
"AddGroupWithOne",
"toAddMonoidWithOne"
],
[
"instDistribLatticeOfLinearOrder"
],
[
"NonUnitalNonAssocRing",
"toNonUnitalNonAssocSemiring"
],
[
"Ring",
... | [
[
"\"Int\"",
"\"fract_nonneg\""
],
[
"\"Ring\"",
"\"toNonAssocRing\""
],
[
"\"PartialOrder\"",
"\"toPreorder\""
],
[
"\"Lattice\"",
"\"toSemilatticeInf\""
],
[
"\"Preorder\"",
"\"toLT\""
],
[
"\"AddGroupWithOne\"",
"\"toAddMonoidWithOne\""
],
[... |
true | theorem | [
"\"AddConstMap\"",
"\"mk\"",
"\"congr_simp\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2840855998._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} (toFun : G -> H) (toFun_1 : G -> H) (e_toFun : Eq.{max (succ u_1) (succ u_2)} (G -> H) toFun to... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (toFun toFun_1 : G → H)
(e_toFun : toFun = toFun_1) (map_add_const' : ∀ (x : G), toFun (x + a) = toFun x + b),
{ toFun := toFun, map_add_const' := map_add_const' } = { toFun := toFun_1, map_add_const' := ⋯ } | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (toFun toFun_1 : G → H)
(e_toFun : toFun = toFun_1) (map_add_const' : ∀ (x : G), toFun (x + a) = toFun x + b),
{ toFun := toFun, map_add_const' := map_add_const' } = { toFun := toFun_1, map_add_const' := ⋯ } | [
[
"HAdd",
"hAdd"
],
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"instHAdd"
],
[
"Add"
],
[
"Eq",
"ndrec"
],
[
"Eq"
]
] | [
[
"\"HAdd\"",
"\"hAdd\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"instHAdd\""
],
[
"\"Eq\"",
"\"refl\""
],
[
"\"Eq\"",
"\"ndrec\""
],
[
"\"Eq\""
],
[
"\"Eq\"",
"\"rec\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"conjNeg\"",
"\"_proof_4\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2537512608._hygCtx._hyg.4 : AddCommGroup.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2537512608._hygCtx._hyg.7 : AddCommGroup.{u_2} H] {a : G} {b : H} (x._@.Mathlib.Algebra.AddConstMap.Basic.2537512608._hygCtx._hyg.62 : AddConst... | ∀ {G : Type u_1} {H : Type u_2} [inst : AddCommGroup G] [inst_1 : AddCommGroup H] {a : G} {b : H}
(x : AddConstMap G H a b),
{ toFun := fun x_1 => -{ toFun := fun x_2 => -x (-x_2), map_add_const' := ⋯ } (-x_1), map_add_const' := ⋯ } = x | ∀ {G : Type u_1} {H : Type u_2} [inst : AddCommGroup G] [inst_1 : AddCommGroup H] {a : G} {b : H}
(x : AddConstMap G H a b),
{ toFun := fun x_1 => -{ toFun := fun x_2 => -x (-x_2), map_add_const' := ⋯ } (-x_1), map_add_const' := ⋯ } = x | [
[
"SubtractionMonoid",
"toSubNegZeroMonoid"
],
[
"AddConstMap"
],
[
"AddConstMap",
"mk"
],
[
"Neg",
"neg"
],
[
"AddConstMap",
"conjNeg",
"_proof_1"
],
[
"AddCommGroup"
],
[
"SubtractionCommMonoid",
"toSubtractionMonoid"
],
[
"DFunLi... | [
[
"\"SubtractionMonoid\"",
"\"toSubNegZeroMonoid\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"Neg\"",
"\"neg\""
],
[
"\"AddConstMap\"",
"\"conjNeg\"",
"\"_proof_1\""
],
[
"\"SubtractionCommMonoid\"",
"\"toSubtractionMonoid\""
... |
true | theorem | [
"\"_private\"",
"\"Mathlib\"",
"\"Algebra\"",
"\"AddConstMap\"",
"\"Basic\"",
"0",
"\"AddConstMapClass\"",
"\"rel_map_of_Icc\"",
"\"_proof_1_2\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1953314843._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {a : G} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1953314843._hygCtx._hyg.12 : AddCommGroup.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} [inst_1 : AddCommGroup G]
[inst_2 : LinearOrder G] [IsOrderedAddMonoid G] {f : F} {R : H → H → Prop} {l : G},
(∀ x ∈ Set.Icc l (l + a), ∀ y ∈ Set.Icc l (l + a), x < y → R (f x) (f y)) →
∀ (x y : G), x ∈ Set.Ico l (l + a) → R (f x) (f ... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {a : G} [inst_1 : AddCommGroup G]
[inst_2 : LinearOrder G] [IsOrderedAddMonoid G] {f : F} {R : H → H → Prop} {l : G},
(∀ x ∈ Set.Icc l (l + a), ∀ y ∈ Set.Icc l (l + a), x < y → R (f x) (f y)) →
∀ (x y : G), x ∈ Set.Ico l (l + a) → R (f x) (f ... | [
[
"PartialOrder",
"toPreorder"
],
[
"Set",
"Icc"
],
[
"AddCommGroup",
"toAddGroup"
],
[
"Membership",
"mem"
],
[
"Preorder",
"toLT"
],
[
"DFunLike",
"coe"
],
[
"instDistribLatticeOfLinearOrder"
],
[
"IsOrderedAddMonoid"
],
[
... | [
[
"\"SubtractionMonoid\"",
"\"toSubNegZeroMonoid\""
],
[
"\"PartialOrder\"",
"\"toPreorder\""
],
[
"\"Eq\"",
"\"trans\""
],
[
"\"Lean\"",
"\"Grind\"",
"\"Order\"",
"\"le_eq_true_of_lt\""
],
[
"\"AddCommGroup\"",
"\"toAddGroup\""
],
[
"\"Members... |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_ofNat'\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2016732250._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] {b : H} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2016732250._hygCtx._hyg.12 : AddMonoidWithOne.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Ba... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddMonoidWithOne G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H 1 b] (f : F) (n : ℕ) [inst_4 : n.AtLeastTwo],
f (OfNat.ofNat n) = f 0 + OfNat.ofNat n • b | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] {b : H} [inst_1 : AddMonoidWithOne G]
[inst_2 : AddMonoid H] [AddConstMapClass F G H 1 b] (f : F) (n : ℕ) [inst_4 : n.AtLeastTwo],
f (OfNat.ofNat n) = f 0 + OfNat.ofNat n • b | [
[
"AddMonoidWithOne",
"toAddMonoid"
],
[
"DFunLike",
"coe"
],
[
"instOfNatNat"
],
[
"Nat",
"AtLeastTwo"
],
[
"instHSMul"
],
[
"Zero",
"toOfNat0"
],
[
"Eq"
],
[
"AddMonoidWithOne"
],
[
"AddSemigroup",
"toAdd"
],
[
"FunLik... | [
[
"\"AddConstMapClass\"",
"\"map_nat'\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_ofNat_add\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.116843649._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] [inst._@.Mathlib.Algebra.AddConstMap.Basic.116843649._hygCtx._hyg.12 : AddCommMonoidWithOne.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.11... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] [inst_1 : AddCommMonoidWithOne G]
[inst_2 : AddMonoidWithOne H] [AddConstMapClass F G H 1 1] (f : F) (n : ℕ) [inst_4 : n.AtLeastTwo] (x : G),
f (OfNat.ofNat n + x) = f x + OfNat.ofNat n | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] [inst_1 : AddCommMonoidWithOne G]
[inst_2 : AddMonoidWithOne H] [AddConstMapClass F G H 1 1] (f : F) (n : ℕ) [inst_4 : n.AtLeastTwo] (x : G),
f (OfNat.ofNat n + x) = f x + OfNat.ofNat n | [
[
"FunLike"
],
[
"instHAdd"
],
[
"instOfNatAtLeastTwo"
],
[
"AddConstMapClass"
],
[
"AddMonoidWithOne",
"toAddMonoid"
],
[
"DFunLike",
"coe"
],
[
"OfNat",
"ofNat"
],
[
"HAdd",
"hAdd"
],
[
"Nat"
],
[
"AddMonoidWithOne",
"... | [
[
"\"AddConstMapClass\"",
"\"map_nat_add\""
]
] |
false | definition | [
"\"AddConstMap\"",
"\"instPowNat\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3231272351._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, Pow.{u_1, 0} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.3231272351._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.3231272351._hygCtx._hyg.4 a a) Nat | {G : Type u_1} → [inst : Add G] → {a : G} → Pow (AddConstMap G G a a) ℕ | {G : Type u_1} → [inst : Add G] → {a : G} → Pow (AddConstMap G G a a) ℕ | [
[
"Nat"
],
[
"AddConstMap"
],
[
"Add"
],
[
"Pow"
]
] | [
[
"\"AddConstMap\"",
"\"instPowNat\"",
"\"_proof_1\""
],
[
"\"Nat\""
],
[
"\"Nat\"",
"\"iterate\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
],
[
... |
true | theorem | [
"\"AddConstMap\"",
"\"toFun_eq_coe\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1270348448._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.1270348448._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} (f : AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.AddConstMap.Basic.1270348448._hygCtx._h... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (f : AddConstMap G H a b), f.toFun = ⇑f | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (f : AddConstMap G H a b), f.toFun = ⇑f | [
[
"AddConstMap"
],
[
"Add"
],
[
"AddConstMap",
"toFun"
],
[
"Eq"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
]
] | [
[
"\"rfl\""
],
[
"\"AddConstMap\"",
"\"toFun\""
]
] |
false | definition | [
"\"AddConstMap\"",
"\"instInhabited\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.4037808124._hygCtx._hyg.4 : Add.{u_1} G] {a : G}, Inhabited.{succ u_1} (AddConstMap.{u_1, u_1} G G inst._@.Mathlib.Algebra.AddConstMap.Basic.4037808124._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AddConstMap.Basic.4037808124._hygCtx._hyg.4 a a) | {G : Type u_1} → [inst : Add G] → {a : G} → Inhabited (AddConstMap G G a a) | {G : Type u_1} → [inst : Add G] → {a : G} → Inhabited (AddConstMap G G a a) | [
[
"AddConstMap"
],
[
"Add"
],
[
"Inhabited"
]
] | [
[
"\"Inhabited\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"id\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"conjNeg\"",
"\"_proof_2\""
] | forall {G : Type.{u_2}} {H : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.2537512608._hygCtx._hyg.4 : AddCommGroup.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.2537512608._hygCtx._hyg.7 : AddCommGroup.{u_1} H] {a : G} {b : H} (x._@.Mathlib.Algebra.AddConstMap.Basic.2537512608._hygCtx._hyg.62 : AddConst... | ∀ {G : Type u_2} {H : Type u_1} [inst : AddCommGroup G] [inst_1 : AddCommGroup H] {a : G} {b : H}
(x : AddConstMap G H a b) (x_1 : G),
-{ toFun := fun x_2 => -x (-x_2), map_add_const' := ⋯ } (-(x_1 + a)) =
-{ toFun := fun x_2 => -x (-x_2), map_add_const' := ⋯ } (-x_1) + b | ∀ {G : Type u_2} {H : Type u_1} [inst : AddCommGroup G] [inst_1 : AddCommGroup H] {a : G} {b : H}
(x : AddConstMap G H a b) (x_1 : G),
-{ toFun := fun x_2 => -x (-x_2), map_add_const' := ⋯ } (-(x_1 + a)) =
-{ toFun := fun x_2 => -x (-x_2), map_add_const' := ⋯ } (-x_1) + b | [
[
"SubtractionMonoid",
"toSubNegZeroMonoid"
],
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"instHAdd"
],
[
"Neg",
"neg"
],
[
"AddConstMap",
"conjNeg",
"_proof_1"
],
[
"AddCommGroup"
],
[
"SubtractionCommMonoid",
"toSubtractionMono... | [
[
"\"SubtractionMonoid\"",
"\"toSubNegZeroMonoid\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"Neg\"",
"\"neg\""
],
[
"\"AddConstMap\"",
"\"conjNeg\"",
"\"_proof_1\""
],
[
"\"SubtractionCommMonoid\"",
"\"toSubtractionMonoid\""
... |
true | theorem | [
"\"_private\"",
"\"Mathlib\"",
"\"Algebra\"",
"\"AddConstMap\"",
"\"Basic\"",
"0",
"\"AddConstMapClass\"",
"\"rel_map_of_Icc\"",
"\"_simp_1_3\""
] | forall {G : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.Defs.2875213658._hygCtx._hyg.3 : AddSemigroup.{u_1} G] (a : G) (b : G) (c : G), Eq.{succ u_1} G (HAdd.hAdd.{u_1, u_1, u_1} G G G (instHAdd.{u_1} G (AddSemigroup.toAdd.{u_1} G inst._@.Mathlib.Algebra.Group.Defs.2875213658._hygCtx._hyg.3)) a (HAdd.hAdd.{u_1, u_1, u_1... | ∀ {G : Type u_1} [inst : AddSemigroup G] (a b c : G), a + (b + c) = a + b + c | ∀ {G : Type u_1} [inst : AddSemigroup G] (a b c : G), a + (b + c) = a + b + c | [
[
"HAdd",
"hAdd"
],
[
"AddSemigroup"
],
[
"instHAdd"
],
[
"Eq"
],
[
"AddSemigroup",
"toAdd"
]
] | [
[
"\"HAdd\"",
"\"hAdd\""
],
[
"\"instHAdd\""
],
[
"\"add_assoc\""
],
[
"\"Eq\"",
"\"symm\""
],
[
"\"AddSemigroup\"",
"\"toAdd\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"mkFract\"",
"\"_proof_1\""
] | forall {R : Type.{u_2}} {G : Type.{u_1}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.4 : Ring.{u_2} R] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3937005748._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R (R... | ∀ {R : Type u_2} {G : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R]
[inst_3 : FloorRing R] [inst_4 : AddGroup G] (a : G) (f : ↑(Set.Ico 0 1) → G) (x : R),
(fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a) (x + 1) = (fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a) x + a | ∀ {R : Type u_2} {G : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R]
[inst_3 : FloorRing R] [inst_4 : AddGroup G] (a : G) (f : ↑(Set.Ico 0 1) → G) (x : R),
(fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a) (x + 1) = (fun x => f ⟨Int.fract x, ⋯⟩ + ⌊x⌋ • a) x + a | [
[
"Ring",
"toNonAssocRing"
],
[
"PartialOrder",
"toPreorder"
],
[
"Membership",
"mem"
],
[
"Preorder",
"toLT"
],
[
"AddGroupWithOne",
"toAddMonoidWithOne"
],
[
"Set",
"Elem"
],
[
"NonUnitalNonAssocRing",
"toNonUnitalNonAssocSemiring"
... | [
[
"\"Ring\"",
"\"toNonAssocRing\""
],
[
"\"PartialOrder\"",
"\"toPreorder\""
],
[
"\"Eq\"",
"\"trans\""
],
[
"\"Membership\"",
"\"mem\""
],
[
"\"Preorder\"",
"\"toLT\""
],
[
"\"Int\"",
"\"floor_add_one\""
],
[
"\"Subtype\"",
"\"mk\"",
... |
true | theorem | [
"\"AddConstMap\"",
"\"mk_coe\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.1564126289._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.1564126289._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} (f : AddConstMap.{u_1, u_2} G H inst._@.Mathlib.Algebra.AddConstMap.Basic.1564126289._hygCtx._h... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (f : AddConstMap G H a b),
{ toFun := ⇑f, map_add_const' := ⋯ } = f | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (f : AddConstMap G H a b),
{ toFun := ⇑f, map_add_const' := ⋯ } = f | [
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"Add"
],
[
"AddConstMap",
"map_add_const'"
],
[
"Eq"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
]
] | [
[
"\"rfl\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"AddConstMap\"",
"\"map_add_const'\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
]
] |
true | theorem | [
"\"AddConstMap\"",
"\"coe_mk\""
] | forall {G : Type.{u_1}} {H : Type.{u_2}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.4209750549._hygCtx._hyg.4 : Add.{u_1} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.4209750549._hygCtx._hyg.7 : Add.{u_2} H] {a : G} {b : H} (f : G -> H) (hf : forall (x : G), Eq.{succ u_2} H (f (HAdd.hAdd.{u_1, u_1, u_1} G G G (instHAd... | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (f : G → H)
(hf : ∀ (x : G), f (x + a) = f x + b), ⇑{ toFun := f, map_add_const' := hf } = f | ∀ {G : Type u_1} {H : Type u_2} [inst : Add G] [inst_1 : Add H] {a : G} {b : H} (f : G → H)
(hf : ∀ (x : G), f (x + a) = f x + b), ⇑{ toFun := f, map_add_const' := hf } = f | [
[
"HAdd",
"hAdd"
],
[
"AddConstMap",
"mk"
],
[
"AddConstMap"
],
[
"instHAdd"
],
[
"Add"
],
[
"Eq"
],
[
"DFunLike",
"coe"
],
[
"AddConstMap",
"instFunLike"
]
] | [
[
"\"rfl\""
],
[
"\"AddConstMap\"",
"\"mk\""
],
[
"\"AddConstMap\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMap\"",
"\"instFunLike\""
]
] |
true | theorem | [
"\"AddConstMapClass\"",
"\"map_nat\""
] | forall {F : Type.{u_1}} {G : Type.{u_2}} {H : Type.{u_3}} [inst._@.Mathlib.Algebra.AddConstMap.Basic.3648731379._hygCtx._hyg.5 : FunLike.{succ u_1, succ u_2, succ u_3} F G H] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3648731379._hygCtx._hyg.12 : AddMonoidWithOne.{u_2} G] [inst._@.Mathlib.Algebra.AddConstMap.Basic.3648... | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] [inst_1 : AddMonoidWithOne G]
[inst_2 : AddMonoidWithOne H] [AddConstMapClass F G H 1 1] (f : F) (n : ℕ), f ↑n = f 0 + ↑n | ∀ {F : Type u_1} {G : Type u_2} {H : Type u_3} [inst : FunLike F G H] [inst_1 : AddMonoidWithOne G]
[inst_2 : AddMonoidWithOne H] [AddConstMapClass F G H 1 1] (f : F) (n : ℕ), f ↑n = f 0 + ↑n | [
[
"FunLike"
],
[
"Nat",
"cast"
],
[
"instHAdd"
],
[
"AddConstMapClass"
],
[
"AddZeroClass",
"toAddZero"
],
[
"AddMonoidWithOne",
"toAddMonoid"
],
[
"DFunLike",
"coe"
],
[
"OfNat",
"ofNat"
],
[
"HAdd",
"hAdd"
],
[
"Na... | [
[
"\"Nat\"",
"\"cast\""
],
[
"\"Eq\"",
"\"trans\""
],
[
"\"AddMonoidWithOne\"",
"\"toAddMonoid\""
],
[
"\"DFunLike\"",
"\"coe\""
],
[
"\"AddConstMapClass\"",
"\"map_nat'\""
],
[
"\"congrArg\""
],
[
"\"instHSMul\""
],
[
"\"Zero\"",
"... |
End of preview.
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