Add files using upload-large-folder tool

.gitattributes

@@ -263,3 +263,15 @@ data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.RingedSpace.OpenI
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 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.ShortComplex.Abelian.sym.json filter=lfs diff=lfs merge=lfs -text
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Algebra.Shrink.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Group.Finset.Lemmas.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.ModEq.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.MonCat.Limits.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.Ring.LinearAlgebra.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Central.Matrix.sym.json

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+[{"isProp":true,"kind":"theorem","name":["Algebra","IsCentral","matrix"],"typeFallback":"forall (K : Type.{u_1}) (D : Type.{u_2}) [inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.4 : CommSemiring.{u_1} K] [inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.7 : Semiring.{u_2} D] [inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.10 : Algebra.{u_1, u_2} K D inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.14 : Algebra.IsCentral.{u_1, u_2} K inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.4 D inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.10] (ι : Type.{u_3}) [inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.19 : Fintype.{u_3} ι] [inst._@.Mathlib.Algebra.Central.Matrix.2395246692._hygCtx._hyg.22 : 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Type.{u_2}} {A : Type.{u_3}} [inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.5 : CommSemiring.{u_2} R] [inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.8 : Semiring.{u_3} A] [inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.11 : Algebra.{u_2, u_3} R A inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.8] [inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.15 : Fintype.{u_1} n] [inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.18 : DecidableEq.{succ u_1} n], Eq.{max (succ u_1) (succ u_3)} (Subalgebra.{u_2, max u_3 u_1} R (Matrix.{u_1, u_1, u_3} n n A) inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.5 (Matrix.semiring.{u_3, u_1} n A inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Central.Matrix.585319887._hygCtx._hyg.18) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharP.Pi.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharP.Subring.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Action.Sigma.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Int.Even.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Int.Units.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.PNatPowAssoc.sym.json

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: Pow M ℕ+] →\n      {motive : PNatPowAssoc M → Sort u} →\n        (t : PNatPowAssoc M) →\n          ((ppow_add : ∀ (k n : ℕ+) (x : M), x ^ (k + n) = x ^ k * x ^ n) →\n              (ppow_one : ∀ (x : M), x ^ 1 = x) → motive ⋯) →\n            motive t","typeReferences":[["instHPow"],["PNatPowAssoc","mk"],["PNat"],["instHAdd"],["Mul"],["HMul","hMul"],["HPow","hPow"],["OfNat","ofNat"],["instAddPNat"],["Nat","instNeZeroSucc"],["HAdd","hAdd"],["Nat"],["instOfNatNat"],["instOfNatPNatOfNeZeroNat"],["PNatPowAssoc"],["Pow"],["instHMul"],["Eq"]],"valueReferences":[["PNatPowAssoc","rec"]]},{"isProp":true,"kind":"definition","name":["PNatPowAssoc","mk","_flat_ctor"],"typeFallback":"forall {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Group.PNatPowAssoc.1971468786._hygCtx._hyg.5 : Mul.{u_2} M] [inst._@.Mathlib.Algebra.Group.PNatPowAssoc.1971468786._hygCtx._hyg.8 : Pow.{u_2, 0} M PNat], (forall (k : PNat) (n : PNat) (x : M), Eq.{succ u_2} M (HPow.hPow.{u_2, 0, u_2} M PNat M (instHPow.{u_2, 0} M PNat 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PNatPowAssoc M → Sort u} →\n        (t : PNatPowAssoc M) →\n          ((ppow_add : ∀ (k n : ℕ+) (x : M), x ^ (k + n) = x ^ k * x ^ n) →\n              (ppow_one : ∀ (x : M), x ^ 1 = x) → motive ⋯) →\n            motive t","typeReferences":[["instHPow"],["PNatPowAssoc","mk"],["PNat"],["instHAdd"],["Mul"],["HMul","hMul"],["HPow","hPow"],["OfNat","ofNat"],["instAddPNat"],["Nat","instNeZeroSucc"],["HAdd","hAdd"],["Nat"],["instOfNatNat"],["instOfNatPNatOfNeZeroNat"],["PNatPowAssoc"],["Pow"],["instHMul"],["Eq"]],"valueReferences":[["PNatPowAssoc","rec"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Translate.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Pi.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.MvPolynomial.Cardinal.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Interval.Finset.Basic.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Finset","image_add_right_Ioo"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.2044909608._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α 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{α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.7))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.19 : DecidableEq.{succ u_2} α] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.image.{u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.19 (fun (x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.36 : α) => HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.4)))) c x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3952387193._hygCtx._hyg.36) (Finset.Ico.{u_2} α (PartialOrder.toPreorder.{u_2} α 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b)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["DecidableEq"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Finset","image"],["PartialOrder"],["Finset","Ico"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["add_right_injective"],["DFunLike","coe"],["congrArg"],["addLeftEmbedding"],["addLeftEmbedding","eq_1"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Function","instFunLikeEmbedding"],["Function","Embedding","mk"],["instHAdd"],["Function","Embedding"],["HAdd","hAdd"],["Finset","map_eq_image"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Finset","Ico"],["Eq","mpr"],["Finset","map_add_left_Ico"],["Function","Embedding","coeFn_mk"]]},{"isProp":true,"kind":"theorem","name":["Finset","image_add_right_Ioc"],"typeFallback":"forall 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[inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.19 : DecidableEq.{succ u_2} α] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.image.{u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.19 (fun (x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.36 : α) => HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.4)))) x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1373940685._hygCtx._hyg.36 c) (Finset.Ioc.{u_2} α (PartialOrder.toPreorder.{u_2} α 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α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => x + c) (Finset.Ioc a b) = Finset.Ioc (a + c) (b + c)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => x + c) (Finset.Ioc a b) = Finset.Ioc (a + c) (b + c)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["DecidableEq"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["Finset","Ioc"],["AddCommMonoid","toAddCommSemigroup"],["Finset","image"],["PartialOrder"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["instIsRightCancelAddOfAddRightReflectLE"],["contravariant_swap_add_of_contravariant_add"],["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["DFunLike","coe"],["congrArg"],["Finset","Ioc"],["addRightEmbedding"],["IsOrderedCancelAddMonoid","toAddLeftReflectLT"],["Eq","symm"],["Finset","map_add_right_Ioc"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Function","instFunLikeEmbedding"],["Eq"],["Preorder","toLE"],["IsLeftCancelAdd","addLeftReflectLE_of_addLeftReflectLT"],["Function","Embedding","mk"],["instHAdd"],["Function","Embedding"],["addRightEmbedding","eq_1"],["Finset","map_eq_image"],["HAdd","hAdd"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["LE","le"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Eq","mpr"],["add_left_injective"],["Function","Embedding","coeFn_mk"]]},{"isProp":true,"kind":"theorem","name":["Finset","map_add_right_Ioc"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7)] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.map.{u_2, u_2} α α (addRightEmbedding.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4))) (instIsRightCancelAddOfAddRightReflectLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7 (contravariant_swap_add_of_contravariant_add.{u_2} α (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : α) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : α) => LE.le.{u_2} α (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7)) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4) (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4))) (instIsLeftCancelAddOfAddLeftReflectLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α 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inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.16 a b)) (Finset.Ioc.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.16 (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4)))) a c) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3748810365._hygCtx._hyg.4)))) b c))","typeFull":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α]\n  [ExistsAddOfLE α] [inst_4 : LocallyFiniteOrder α] (a b c : α),\n  Finset.map (addRightEmbedding c) (Finset.Ioc a b) = Finset.Ioc (a + c) (b + c)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α]\n  [ExistsAddOfLE α] [inst_4 : LocallyFiniteOrder α] (a b c : α),\n  Finset.map (addRightEmbedding c) (Finset.Ioc a b) = Finset.Ioc (a + c) (b + c)","typeReferences":[["contravariant_swap_add_of_contravariant_add"],["instIsRightCancelAddOfAddRightReflectLE"],["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["Finset","Ioc"],["AddCommMonoid","toAddCommSemigroup"],["PartialOrder"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["LE","le"],["IsOrderedCancelAddMonoid","toAddLeftReflectLT"],["addRightEmbedding"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["IsLeftCancelAdd","addLeftReflectLE_of_addLeftReflectLT"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["contravariant_swap_add_of_contravariant_add"],["instIsRightCancelAddOfAddRightReflectLE"],["Finset","instSetLike"],["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["Finset","coe_Ioc"],["Finset","coe_map"],["DFunLike","coe"],["congrArg"],["Finset","Ioc"],["Eq","symm"],["addRightEmbedding"],["IsOrderedCancelAddMonoid","toAddLeftReflectLT"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Function","instFunLikeEmbedding"],["Preorder","toLE"],["Eq"],["IsLeftCancelAdd","addLeftReflectLE_of_addLeftReflectLT"],["propext"],["Finset","coe_inj"],["instHAdd"],["Set"],["Function","Embedding"],["HAdd","hAdd"],["Set","image_add_const_Ioc"],["Set","image"],["SetLike","coe"],["AddCommMonoid","toAddCommSemigroup"],["Set","Ioc"],["LE","le"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["Finset","image_add_left_Ioo"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.7))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.19 : DecidableEq.{succ u_2} α] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.image.{u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.19 (fun (x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.36 : α) => HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.4)))) c x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.36) (Finset.Ioo.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.16 a b)) (Finset.Ioo.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.16 (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.4)))) c a) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.17055235._hygCtx._hyg.4)))) c b))","typeFull":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => c + x) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + b)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => c + x) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + b)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["DecidableEq"],["HAdd","hAdd"],["LocallyFiniteOrder"],["Finset","Ioo"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Finset","image"],["PartialOrder"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["add_right_injective"],["DFunLike","coe"],["congrArg"],["addLeftEmbedding"],["addLeftEmbedding","eq_1"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Function","instFunLikeEmbedding"],["Finset","map_add_left_Ioo"],["Function","Embedding","mk"],["instHAdd"],["Function","Embedding"],["HAdd","hAdd"],["Finset","map_eq_image"],["Finset","Ioo"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Eq","mpr"],["Function","Embedding","coeFn_mk"]]},{"isProp":true,"kind":"theorem","name":["Finset","image_add_right_Ico"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.7))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.19 : DecidableEq.{succ u_2} α] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.image.{u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.19 (fun (x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.36 : α) => HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.4)))) x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.242491874._hygCtx._hyg.36 c) (Finset.Ico.{u_2} α (PartialOrder.toPreorder.{u_2} α 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[inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => x + c) (Finset.Ico a b) = Finset.Ico (a + c) (b + c)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => x + c) (Finset.Ico a b) = Finset.Ico (a + c) (b + c)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["DecidableEq"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Finset","image"],["PartialOrder"],["Finset","Ico"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["instIsRightCancelAddOfAddRightReflectLE"],["contravariant_swap_add_of_contravariant_add"],["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["DFunLike","coe"],["congrArg"],["addRightEmbedding"],["IsOrderedCancelAddMonoid","toAddLeftReflectLT"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Function","instFunLikeEmbedding"],["Eq"],["Preorder","toLE"],["IsLeftCancelAdd","addLeftReflectLE_of_addLeftReflectLT"],["Function","Embedding","mk"],["instHAdd"],["Finset","map_add_right_Ico"],["Function","Embedding"],["addRightEmbedding","eq_1"],["Finset","map_eq_image"],["HAdd","hAdd"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["LE","le"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Finset","Ico"],["Eq","mpr"],["add_left_injective"],["Function","Embedding","coeFn_mk"]]},{"isProp":true,"kind":"theorem","name":["Finset","map_add_right_Ico"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.4222126885._hygCtx._hyg.7))] 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(addRightEmbedding c) (Finset.Ico a b) = Finset.Ico (a + c) (b + c)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α]\n  [ExistsAddOfLE α] [inst_4 : LocallyFiniteOrder α] (a b c : α),\n  Finset.map (addRightEmbedding c) (Finset.Ico a b) = Finset.Ico (a + c) (b + 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{α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7)] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.map.{u_2, u_2} α α (addLeftEmbedding.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4))) (instIsLeftCancelAddOfAddLeftReflectLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7 (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.10)) c) (Finset.Ico.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.16 a b)) (Finset.Ico.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.16 (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.361039034._hygCtx._hyg.4)))) c a) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α 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b)","typeReferences":[["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["addLeftEmbedding"],["AddCommMonoid","toAddCommSemigroup"],["PartialOrder"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["Finset","Ico"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["Finset","instSetLike"],["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["Finset","coe_Ico"],["Finset","coe_map"],["DFunLike","coe"],["congrArg"],["addLeftEmbedding"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Set","Ico"],["Function","instFunLikeEmbedding"],["Eq"],["propext"],["Finset","coe_inj"],["Set","image_const_add_Ico"],["instHAdd"],["Set"],["Function","Embedding"],["HAdd","hAdd"],["Set","image"],["SetLike","coe"],["AddCommMonoid","toAddCommSemigroup"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["id"],["Finset","Ico"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["Finset","image_add_left_Icc"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1310589756._hygCtx._hyg.7))] 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α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => c + x) (Finset.Icc a b) = Finset.Icc (c + a) (c + b)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => c + x) (Finset.Icc a b) = Finset.Icc (c + a) (c + b)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["DecidableEq"],["Finset","Icc"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Finset","image"],["PartialOrder"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["add_right_injective"],["DFunLike","coe"],["congrArg"],["addLeftEmbedding"],["addLeftEmbedding","eq_1"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Function","instFunLikeEmbedding"],["Function","Embedding","mk"],["instHAdd"],["Function","Embedding"],["Finset","Icc"],["HAdd","hAdd"],["Finset","map_eq_image"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Eq","mpr"],["Finset","map_add_left_Icc"],["Function","Embedding","coeFn_mk"]]},{"isProp":true,"kind":"theorem","name":["Finset","map_add_right_Icc"],"typeFallback":"forall 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[inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.7)] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.map.{u_2, u_2} α α (addLeftEmbedding.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.4))) (instIsLeftCancelAddOfAddLeftReflectLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.7 (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α 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inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.447462470._hygCtx._hyg.4)))) c b))","typeFull":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α]\n  [ExistsAddOfLE α] [inst_4 : LocallyFiniteOrder α] (a b c : α),\n  Finset.map (addLeftEmbedding c) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + b)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α]\n  [ExistsAddOfLE α] [inst_4 : LocallyFiniteOrder α] (a b c : α),\n  Finset.map (addLeftEmbedding c) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + 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{α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1992258354._hygCtx._hyg.7))] 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(addRightEmbedding c) (Finset.Ioo a b) = Finset.Ioo (a + c) (b + c)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelAddMonoid α]\n  [ExistsAddOfLE α] [inst_4 : LocallyFiniteOrder α] (a b c : α),\n  Finset.map (addRightEmbedding c) (Finset.Ioo a b) = Finset.Ioo (a + c) (b + 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[inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.19 : DecidableEq.{succ u_2} α] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.image.{u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.19 (fun (x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.36 : α) => HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.4)))) x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1400047987._hygCtx._hyg.36 c) (Finset.Icc.{u_2} α (PartialOrder.toPreorder.{u_2} α 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α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => x + c) (Finset.Icc a b) = Finset.Icc (a + c) (b + c)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => x + c) (Finset.Icc a b) = Finset.Icc (a + c) (b + 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[inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.7)] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.map.{u_2, u_2} α α (addLeftEmbedding.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.4))) (instIsLeftCancelAddOfAddLeftReflectLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.7 (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.10)) c) (Finset.Icc.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.16 a b)) (Finset.Icc.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.16 (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.3483033856._hygCtx._hyg.4)))) c a) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α 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b)","typeReferences":[["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["Finset","Icc"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["addLeftEmbedding"],["AddCommMonoid","toAddCommSemigroup"],["PartialOrder"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["Finset","instSetLike"],["Set","image_const_add_Icc"],["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["Set","Icc"],["Finset","coe_map"],["DFunLike","coe"],["Finset","coe_Icc"],["congrArg"],["addLeftEmbedding"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Function","instFunLikeEmbedding"],["Eq"],["propext"],["Finset","coe_inj"],["instHAdd"],["Set"],["Function","Embedding"],["Finset","Icc"],["HAdd","hAdd"],["Set","image"],["SetLike","coe"],["AddCommMonoid","toAddCommSemigroup"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["id"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["Finset","image_add_left_Ioc"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.4 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.7 : PartialOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.4 (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.13 : ExistsAddOfLE.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.4))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.7))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.16 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.19 : DecidableEq.{succ u_2} α] (a : α) (b : α) (c : α), Eq.{succ u_2} (Finset.{u_2} α) (Finset.image.{u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.19 (fun (x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.36 : α) => HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.4)))) c x._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.36) (Finset.Ioc.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.16 a b)) (Finset.Ioc.{u_2} α (PartialOrder.toPreorder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.16 (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.4)))) c a) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.Basic.1241062420._hygCtx._hyg.4)))) c b))","typeFull":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => c + x) (Finset.Ioc a b) = Finset.Ioc (c + a) (c + b)","typeReadable":"∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]\n  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),\n  Finset.image (fun x => c + x) (Finset.Ioc a b) = Finset.Ioc (c + a) (c + b)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["instHAdd"],["DecidableEq"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["Finset","Ioc"],["AddCommMonoid","toAddCommSemigroup"],["Finset","image"],["PartialOrder"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["Finset","map"],["PartialOrder","toPreorder"],["Finset"],["add_right_injective"],["DFunLike","coe"],["congrArg"],["addLeftEmbedding"],["Finset","Ioc"],["addLeftEmbedding","eq_1"],["Eq","symm"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Function","instFunLikeEmbedding"],["Function","Embedding","mk"],["instHAdd"],["Function","Embedding"],["HAdd","hAdd"],["Finset","map_eq_image"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["instIsLeftCancelAddOfAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["id"],["Finset","map_add_left_Ioc"],["Eq","mpr"],["Function","Embedding","coeFn_mk"]]}]