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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Algebra.Hom.Rat.sym.json

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+[{"isProp":true,"kind":"theorem","name":["AlgHom","toRingHom_toRatAlgHom"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.4 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.7 : Ring.{u_2} S] [inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.10 : Algebra.{0, u_1} Rat R Rat.commSemiring (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.4)] [inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.16 : Algebra.{0, u_2} Rat S Rat.commSemiring (Ring.toSemiring.{u_2} S inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.7)] (f : AlgHom.{0, u_1, u_2} Rat R S Rat.commSemiring (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.4) (Ring.toSemiring.{u_2} S inst._@.Mathlib.Algebra.Algebra.Hom.Rat.2143817852._hygCtx._hyg.7) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.AlgebraicCard.sym.json

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+[{"isProp":true,"kind":"theorem","name":["Algebraic","cardinalMk_le_mul"],"typeFallback":"forall (R : Type.{u}) (A : Type.{u}) [inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.10 : CommRing.{u} A] [inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.13 : IsDomain.{u} A (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.16 : Algebra.{u, u} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4) (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.20 : Module.IsTorsionFree.{u, u} R A (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} A (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u} A (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u} A (CommRing.toNonUnitalCommRing.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.10))))) (Algebra.toModule.{u, u} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4) (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.16)], LE.le.{succ u} Cardinal.{u} Cardinal.instLE.{u} (Cardinal.mk.{u} (Subtype.{succ u} A (fun (x : A) => IsAlgebraic.{u, u} R A inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4 (CommRing.toRing.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.10) inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.16 x))) (HMul.hMul.{succ u, succ u, succ u} Cardinal.{u} Cardinal.{u} Cardinal.{u} (instHMul.{succ u} Cardinal.{u} Cardinal.instMul.{u}) (Cardinal.mk.{u} (Polynomial.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.3505541373._hygCtx._hyg.4)))) Cardinal.aleph0.{u})","typeFull":"∀ (R A : Type u) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A], Cardinal.mk { x // IsAlgebraic R x } ≤ Cardinal.mk (Polynomial R) * Cardinal.aleph0","typeReadable":"∀ (R A : Type u) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree 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(R : Type.{u_1}) (A : Type.{u_2}) [inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.4 : CommRing.{u_1} R] [inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.7 : Ring.{u_2} A] [inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.10 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.4) (Ring.toSemiring.{u_2} A inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.14 : CharZero.{u_2} A (AddGroupWithOne.toAddMonoidWithOne.{u_2} A (Ring.toAddGroupWithOne.{u_2} A inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.7))], Set.Infinite.{u_2} A (setOf.{u_2} A (fun (x : A) => IsAlgebraic.{u_1, u_2} R A inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.4 inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.7 inst._@.Mathlib.Algebra.AlgebraicCard.791726243._hygCtx._hyg.10 x))","typeFull":"∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [CharZero A],\n  {x | IsAlgebraic R x}.Infinite","typeReadable":"∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] [CharZero A],\n  {x | IsAlgebraic R x}.Infinite","typeReferences":[["CommRing","toCommSemiring"],["Ring","toAddGroupWithOne"],["IsAlgebraic"],["Set","Infinite"],["AddGroupWithOne","toAddMonoidWithOne"],["CharZero"],["CommRing"],["setOf"],["Ring","toSemiring"],["Algebra"],["Ring"]],"valueReferences":[["Nat","cast_injective"],["Nat","cast"],["Set","infinite_of_injective_forall_mem"],["Ring","toNonAssocRing"],["instInfiniteNat"],["isAlgebraic_nat"],["instNontrivialOfCharZero"],["AddGroupWithOne","toAddMonoidWithOne"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["Algebra","toModule"],["MulActionWithZero","nontrivial"],["NonAssocRing","toNonUnitalNonAssocRing"],["CommRing","toCommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["Module","toMulActionWithZero"],["Ring","toSemiring"],["Nat"],["AddMonoidWithOne","toNatCast"],["IsAlgebraic"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["setOf"]]},{"isProp":true,"kind":"theorem","name":["Algebraic","cardinalMk_of_infinite"],"typeFallback":"forall (R : Type.{u}) (A : Type.{u}) [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.10 : CommRing.{u} A] [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.13 : IsDomain.{u} A (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.16 : Algebra.{u, u} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.4) (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.20 : Module.IsTorsionFree.{u, u} R A (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} A (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u} A (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u} A (CommRing.toNonUnitalCommRing.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.10))))) (Algebra.toModule.{u, u} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.4) (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.16)] [inst._@.Mathlib.Algebra.AlgebraicCard.417227663._hygCtx._hyg.24 : Infinite.{succ u} R], Eq.{succ (succ u)} Cardinal.{u} (Cardinal.mk.{u} (Subtype.{succ u} A (fun (x : A) => IsAlgebraic.{u, u} R A 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R","typeReferences":[["Module","IsTorsionFree"],["CommRing","toCommSemiring"],["Subtype"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["IsDomain"],["CommRing","toNonUnitalCommRing"],["CommRing"],["Cardinal"],["Cardinal","mk"],["Algebra"],["CommRing","toRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["IsAlgebraic"],["Algebra","toModule"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Eq"],["Infinite"]],"valueReferences":[["CommRing","toRing"],["Subtype"],["Cardinal","lift_inj"],["Cardinal","lift"],["IsAlgebraic"],["Algebraic","cardinalMk_lift_of_infinite"],["Iff","mp"],["Eq"],["Cardinal"],["Cardinal","mk"]]},{"isProp":true,"kind":"theorem","name":["Algebraic","cardinalMk_of_countable_of_charZero"],"typeFallback":"forall (R : Type.{u}) (A : Type.{v}) [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10 : CommRing.{v} A] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.13 : IsDomain.{v} A (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.16 : Algebra.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.20 : Module.IsTorsionFree.{u, v} R A (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{v} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{v} A (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{v} A (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{v} A (CommRing.toNonUnitalCommRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10))))) (Algebra.toModule.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.16)] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.24 : Countable.{succ u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.27 : CharZero.{v} A (AddGroupWithOne.toAddMonoidWithOne.{v} A (Ring.toAddGroupWithOne.{v} A (CommRing.toRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10)))], Eq.{succ (succ v)} Cardinal.{v} (Cardinal.mk.{v} (Subtype.{succ v} A (fun (x : A) => IsAlgebraic.{u, v} R A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.4 (CommRing.toRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.10) inst._@.Mathlib.Algebra.AlgebraicCard.2368028011._hygCtx._hyg.16 x))) Cardinal.aleph0.{v}","typeFull":"∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A] [Countable R] [CharZero A], Cardinal.mk { x // IsAlgebraic R x } = Cardinal.aleph0","typeReadable":"∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A] [Countable R] [CharZero A], Cardinal.mk { x // IsAlgebraic R x } = 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(R : Type.{u}) (A : Type.{v}) [inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.10 : CommRing.{v} A] [inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.13 : IsDomain.{v} A (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.16 : Algebra.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.20 : Module.IsTorsionFree.{u, v} R A (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{v} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{v} A (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{v} A (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{v} A (CommRing.toNonUnitalCommRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.10))))) (Algebra.toModule.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.16)], LE.le.{max (succ u) (succ v)} Cardinal.{max v u} Cardinal.instLE.{max u v} (Cardinal.lift.{u, v} (Cardinal.mk.{v} (Subtype.{succ v} A (fun (x : A) => IsAlgebraic.{u, v} R A inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.4 (CommRing.toRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.10) inst._@.Mathlib.Algebra.AlgebraicCard.2420575835._hygCtx._hyg.16 x)))) (Max.max.{max (succ v) (succ u)} Cardinal.{max u v} (SemilatticeSup.toMax.{max (succ u) (succ v)} Cardinal.{max u v} (Lattice.toSemilatticeSup.{max (succ u) (succ v)} Cardinal.{max u v} (ConditionallyCompleteLattice.toLattice.{max (succ u) (succ v)} Cardinal.{max u v} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u) (succ v)} Cardinal.{max u v} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u) (succ v)} Cardinal.{max u v} Cardinal.instConditionallyCompleteLinearOrderBot.{max u v}))))) (Cardinal.lift.{v, u} (Cardinal.mk.{u} R)) Cardinal.aleph0.{max u v})","typeFull":"∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A],\n  Cardinal.lift.{u, v} (Cardinal.mk { x // IsAlgebraic R x }) ≤\n    max (Cardinal.lift.{v, u} (Cardinal.mk R)) Cardinal.aleph0","typeReadable":"∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A],\n  Cardinal.lift.{u, v} (Cardinal.mk { x // IsAlgebraic R x }) ≤\n    max (Cardinal.lift.{v, u} (Cardinal.mk R)) 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(R : Type.{u}) (A : Type.{v}) [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.10 : CommRing.{v} A] [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.13 : IsDomain.{v} A (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.16 : Algebra.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.20 : Module.IsTorsionFree.{u, v} R A (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{v} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{v} A (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{v} A (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{v} A (CommRing.toNonUnitalCommRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.10))))) (Algebra.toModule.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.16)] [inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.24 : Infinite.{succ u} R], Eq.{max (succ (succ u)) (succ (succ v))} Cardinal.{max v u} (Cardinal.lift.{u, v} (Cardinal.mk.{v} (Subtype.{succ v} A (fun (x : A) => IsAlgebraic.{u, v} R A inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.4 (CommRing.toRing.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.10) inst._@.Mathlib.Algebra.AlgebraicCard.381974436._hygCtx._hyg.16 x)))) (Cardinal.lift.{v, u} (Cardinal.mk.{u} R))","typeFull":"∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A] [Infinite R],\n  Cardinal.lift.{u, v} (Cardinal.mk { x // IsAlgebraic R x }) = Cardinal.lift.{v, u} (Cardinal.mk R)","typeReadable":"∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A] [Infinite R],\n  Cardinal.lift.{u, v} (Cardinal.mk { x // IsAlgebraic R x }) = Cardinal.lift.{v, u} (Cardinal.mk R)","typeReferences":[["Module","IsTorsionFree"],["CommRing","toCommSemiring"],["Subtype"],["Cardinal","lift"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["IsDomain"],["CommRing","toNonUnitalCommRing"],["CommRing"],["Cardinal"],["Cardinal","mk"],["Algebra"],["CommRing","toRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["IsAlgebraic"],["Algebra","toModule"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Eq"],["Infinite"]],"valueReferences":[["RingHom"],["Lattice","toSemilatticeSup"],["LE","le","trans_eq"],["Subtype"],["Cardinal","lift"],["Cardinal","aleph0"],["Iff","mp"],["RingHom","instFunLike"],["Cardinal","aleph0_le_mk"],["Cardinal","linearOrder"],["Subtype","val"],["DFunLike","coe"],["Cardinal","mk"],["Cardinal","partialOrder"],["Nonempty","intro"],["Semiring","toNonAssocSemiring"],["ConditionallyCompleteLinearOrder","toConditionallyCompleteLattice"],["instInfiniteULift"],["LE","le","antisymm"],["Eq"],["max_eq_left"],["Cardinal","instLE"],["IsDomain","toNontrivial"],["CommRing","toCommSemiring"],["Function","Embedding","mk"],["FaithfulSMul","algebraMap_injective"],["Subtype","ext_iff"],["ULift"],["CommSemiring","toSemiring"],["Function","Embedding"],["Nonempty"],["Module","IsTorsionFree","to_faithfulSMul"],["Cardinal"],["Cardinal","lift_mk_le'"],["CommRing","toRing"],["Max","max"],["IsAlgebraic"],["Iff","mpr"],["LE","le"],["SemilatticeSup","toMax"],["Cardinal","instConditionallyCompleteLinearOrderBot"],["Subtype","mk"],["ConditionallyCompleteLattice","toLattice"],["ConditionallyCompleteLinearOrderBot","toConditionallyCompleteLinearOrder"],["IsDomain","toIsCancelMulZero"],["isAlgebraic_algebraMap"],["Algebraic","cardinalMk_lift_le_max"],["algebraMap"]]},{"isProp":true,"kind":"theorem","name":["Algebraic","cardinalMk_le_max"],"typeFallback":"forall (R : Type.{u}) (A : Type.{u}) [inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.10 : CommRing.{u} A] [inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.13 : IsDomain.{u} A (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.16 : Algebra.{u, u} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.4) (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.20 : Module.IsTorsionFree.{u, u} R A (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u} A (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u} A (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u} A (CommRing.toNonUnitalCommRing.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.10))))) (Algebra.toModule.{u, u} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.4) (CommSemiring.toSemiring.{u} A (CommRing.toCommSemiring.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.10)) inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.16)], LE.le.{succ u} Cardinal.{u} Cardinal.instLE.{u} (Cardinal.mk.{u} (Subtype.{succ u} A (fun (x : A) => IsAlgebraic.{u, u} R A inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.4 (CommRing.toRing.{u} A inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.10) inst._@.Mathlib.Algebra.AlgebraicCard.2753875788._hygCtx._hyg.16 x))) (Max.max.{succ u} Cardinal.{u} (SemilatticeSup.toMax.{succ u} Cardinal.{u} (Lattice.toSemilatticeSup.{succ u} Cardinal.{u} (ConditionallyCompleteLattice.toLattice.{succ u} Cardinal.{u} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u} Cardinal.{u} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u} Cardinal.{u} Cardinal.instConditionallyCompleteLinearOrderBot.{u}))))) (Cardinal.mk.{u} R) Cardinal.aleph0.{u})","typeFull":"∀ (R A : Type u) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A], Cardinal.mk { x // IsAlgebraic R x } ≤ max (Cardinal.mk R) Cardinal.aleph0","typeReadable":"∀ (R A : Type u) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]\n  [Module.IsTorsionFree R A], Cardinal.mk { x // IsAlgebraic R x } ≤ max (Cardinal.mk R) Cardinal.aleph0","typeReferences":[["Module","IsTorsionFree"],["Lattice","toSemilatticeSup"],["Subtype"],["Cardinal","aleph0"],["IsDomain"],["CommRing","toNonUnitalCommRing"],["Cardinal","mk"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["ConditionallyCompleteLinearOrder","toConditionallyCompleteLattice"],["Algebra","toModule"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Cardinal","instLE"],["CommRing","toCommSemiring"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["CommRing"],["Cardinal"],["Algebra"],["CommRing","toRing"],["Max","max"],["IsAlgebraic"],["LE","le"],["SemilatticeSup","toMax"],["Cardinal","instConditionallyCompleteLinearOrderBot"],["ConditionallyCompleteLattice","toLattice"],["ConditionallyCompleteLinearOrderBot","toConditionallyCompleteLinearOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["Subtype"],["Cardinal","lift_id"],["Cardinal","lift"],["Cardinal","aleph0"],["Cardinal"],["congrArg"],["Cardinal","mk"],["CommRing","toRing"],["Max","max"],["ConditionallyCompleteLinearOrder","toConditionallyCompleteLattice"],["IsAlgebraic"],["LE","le"],["SemilatticeSup","toMax"],["Eq","symm"],["id"],["Cardinal","instConditionallyCompleteLinearOrderBot"],["Eq","mpr"],["ConditionallyCompleteLinearOrderBot","toConditionallyCompleteLinearOrder"],["ConditionallyCompleteLattice","toLattice"],["Eq"],["Algebraic","cardinalMk_lift_le_max"],["Cardinal","instLE"]]},{"isProp":true,"kind":"theorem","name":["Algebraic","countable","_simp_1"],"typeFallback":"forall (R : Type.{u}) (A : Type.{v}) [inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.7 : IsDomain.{u} R (CommSemiring.toSemiring.{u} R (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.4))] [inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.10 : CommRing.{v} A] [inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.13 : IsDomain.{v} A (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.16 : Algebra.{u, v} R A (CommRing.toCommSemiring.{u} R inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.4) (CommSemiring.toSemiring.{v} A (CommRing.toCommSemiring.{v} A inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.10))] [inst._@.Mathlib.Algebra.AlgebraicCard.319944585._hygCtx._hyg.20 : 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.EnoughInjectives.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.LeftResolution.sym.json

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inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3))) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (fun (X : ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (Y : ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) => LinearMap.instFunLike.{u_1, u_1, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y)) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (ModuleCat.free.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (ModuleCat.projectiveResolution._proof_1.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (CategoryTheory.ObjectProperty.ι.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.isProjective.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)))) X) (CategoryTheory.Functor.obj.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.Functor.id.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) X) (CategoryTheory.NatTrans.app.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.Functor.comp.{u_1, u_1, u_1, succ u_1, succ u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.ObjectProperty.FullSubcategory.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.isProjective.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3))) (CategoryTheory.ObjectProperty.FullSubcategory.category.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.isProjective.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3))) (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.ObjectProperty.lift.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.isProjective.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (CategoryTheory.Functor.comp.{u_1, u_1, u_1, succ u_1, succ u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) Type.{u_1} CategoryTheory.types.{u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.forget.{u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) => LinearMap.{u_1, u_1, u_1, u_1} R R (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3))) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (fun (X : ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (Y : ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) => LinearMap.instFunLike.{u_1, u_1, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X) (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y) (ModuleCat.isAddCommGroup.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y)) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 X) (ModuleCat.isModule.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3 Y) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (ModuleCat.free.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (ModuleCat.projectiveResolution._proof_1.{u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3)) (CategoryTheory.ObjectProperty.ι.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (ModuleCat.moduleCategory.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) (CategoryTheory.isProjective.{u_1, succ u_1} (ModuleCat.{u_1, u_1} R inst._@.Mathlib.Algebra.Category.ModuleCat.LeftResolution.2380987969._hygCtx._hyg.3) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharP.CharAndCard.sym.json

@@ -0,0 +1 @@
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(R : Type.{u_1}) [inst._@.Mathlib.Algebra.CharP.CharAndCard.3874901653._hygCtx._hyg.3 : CommRing.{u_1} R] (p : Nat) [inst._@.Mathlib.Algebra.CharP.CharAndCard.3874901653._hygCtx._hyg.9 : Fact (Nat.Prime p)] [inst._@.Mathlib.Algebra.CharP.CharAndCard.3874901653._hygCtx._hyg.12 : Finite.{succ u_1} R], Iff (IsUnit.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.CharP.CharAndCard.3874901653._hygCtx._hyg.3)))) (Nat.cast.{u_1} R (AddMonoidWithOne.toNatCast.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R (CommRing.toRing.{u_1} R inst._@.Mathlib.Algebra.CharP.CharAndCard.3874901653._hygCtx._hyg.3)))) p)) (Not (Dvd.dvd.{0} Nat Nat.instDvd p (ringChar.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R 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[inst._@.Mathlib.Algebra.CharP.CharAndCard.2790914671._hygCtx._hyg.6 : IsDomain.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.CharP.CharAndCard.2790914671._hygCtx._hyg.3))] [inst._@.Mathlib.Algebra.CharP.CharAndCard.2790914671._hygCtx._hyg.9 : Fintype.{u_1} R] {p : Nat} {f : Nat} [hp : Fact (Nat.Prime p)], (Eq.{1} Nat (Fintype.card.{u_1} R inst._@.Mathlib.Algebra.CharP.CharAndCard.2790914671._hygCtx._hyg.9) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.toPow.{0} Nat Nat.instMonoid)) p f)) -> (CharP.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R (CommRing.toRing.{u_1} R inst._@.Mathlib.Algebra.CharP.CharAndCard.2790914671._hygCtx._hyg.3))) p)","typeFull":"∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [inst_2 : Fintype R] {p f : ℕ} [hp : Fact (Nat.Prime p)],\n  Fintype.card R = p ^ f → CharP R p","typeReadable":"∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [inst_2 : Fintype R] {p f : ℕ} [hp : Fact (Nat.Prime p)],\n  Fintype.card R = p ^ f → CharP R 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Field.Equiv.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["MulEquiv","isField"],"typeFallback":"forall {A : Type.{u_1}} {B : Type.{u_2}} [inst._@.Mathlib.Algebra.Field.Equiv.3299413866._hygCtx._hyg.5 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Field.Equiv.3299413866._hygCtx._hyg.8 : Semiring.{u_2} B], (IsField.{u_2} B inst._@.Mathlib.Algebra.Field.Equiv.3299413866._hygCtx._hyg.8) -> (MulEquiv.{u_1, u_2} A B (Distrib.toMul.{u_1} A (NonUnitalNonAssocSemiring.toDistrib.{u_1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Field.Equiv.3299413866._hygCtx._hyg.5)))) (Distrib.toMul.{u_2} B (NonUnitalNonAssocSemiring.toDistrib.{u_2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} B (Semiring.toNonAssocSemiring.{u_2} B inst._@.Mathlib.Algebra.Field.Equiv.3299413866._hygCtx._hyg.8))))) -> (IsField.{u_1} A inst._@.Mathlib.Algebra.Field.Equiv.3299413866._hygCtx._hyg.5)","typeFull":"∀ {A : Type u_1} {B : Type u_2} [inst : Semiring A] [inst_1 : Semiring B], IsField B → ∀ (e : A ≃* B), IsField A","typeReadable":"∀ {A : Type u_1} {B : Type u_2} [inst : Semiring A] [inst_1 : Semiring B], IsField B → ∀ (e : A ≃* B), IsField A","typeReferences":[["Semiring","toNonAssocSemiring"],["MulEquiv"],["NonUnitalNonAssocSemiring","toDistrib"],["IsField"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["Semiring"]],"valueReferences":[["IsLocalHom","isField"],["MulEquiv"],["MulEquivClass","toMonoidWithZeroHomClass"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Semiring","toMonoidWithZero"],["MulEquiv","instEquivLike"],["MulEquiv","instMulEquivClass"],["Semiring","toNonAssocSemiring"],["MulEquiv","injective"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["isLocalHom_equiv"],["NonAssocSemiring","toMulZeroOneClass"]]},{"isProp":true,"kind":"theorem","name":["IsLocalHom","isField"],"typeFallback":"forall {A : Type.{u_1}} {B : Type.{u_2}} {F : Type.{u_3}} [inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.5 : Semiring.{u_1} A] [inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.8 : Semiring.{u_2} B] [inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.11 : FunLike.{succ u_3, succ u_1, succ u_2} F A B] [inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.16 : MonoidWithZeroHomClass.{u_3, u_1, u_2} F A B (NonAssocSemiring.toMulZeroOneClass.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.5)) (NonAssocSemiring.toMulZeroOneClass.{u_2} B (Semiring.toNonAssocSemiring.{u_2} B inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.8)) inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.11] {f : F} [inst._@.Mathlib.Algebra.Field.Equiv.3299413865._hygCtx._hyg.22 : IsLocalHom.{u_1, u_2, u_3} A B F (MonoidWithZero.toMonoid.{u_1} A (Semiring.toMonoidWithZero.{u_1} A 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Action.Sum.sym.json

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Semiconj.Basic.sym.json

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

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Submonoid.DistribMulAction.sym.json

@@ -0,0 +1 @@
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[inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.4 : Monoid.{u_1} M] {S : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.8 : SetLike.{u_3, u_1} S M] (s : S) [inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.13 : SubmonoidClass.{u_3, u_1} S M (Monoid.toMulOneClass.{u_1} M inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.8] [inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.17 : AddMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.20 : DistribMulAction.{u_1, u_2} M α inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.17], DistribMulAction.{u_1, u_2} (Subtype.{succ u_1} M (fun 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: SubmonoidClass S M] → [inst_3 : AddMonoid α] → [DistribMulAction M α] → DistribMulAction (↥s) α","typeReferences":[["SetLike","instMembership"],["Subtype"],["SubmonoidClass","toMonoid"],["Membership","mem"],["Monoid","toMulOneClass"],["Monoid"],["AddMonoid"],["SetLike"],["SubmonoidClass"],["DistribMulAction"]],"valueReferences":[["Submonoid","instDistribMulActionSubtypeMem","_proof_2"],["Submonoid","instDistribMulActionSubtypeMem","_proof_1"],["SetLike","instMembership"],["Subtype"],["SubmonoidClass","toMonoid"],["Membership","mem"],["DistribMulAction","toMulAction"],["DistribMulAction","mk"],["Submonoid","instMulActionSubtypeMem"]]},{"isProp":true,"kind":"theorem","name":["Submonoid","instDistribMulActionSubtypeMem","_proof_1"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.4 : Monoid.{u_1} M] {S : Type.{u_2}} [inst._@.Mathlib.Algebra.Group.Submonoid.DistribMulAction.3281946501._hygCtx._hyg.8 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Action.ConjAct.sym.json

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

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

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

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.Factorizations.Basic.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.PointwisePi.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Presentation.Finite.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Archimedean.IndicatorCard.sym.json

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+[{"isProp":true,"kind":"theorem","name":["Set","infinite_iff_tendsto_sum_indicator_atTop"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.3 : AddCommMonoid.{u_1} R] [inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.6 : PartialOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.9 : IsOrderedAddMonoid.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.3 (PartialOrder.toPreorder.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.12 : AddLeftStrictMono.{u_1} R (AddCommMagma.toAdd.{u_1} R (AddCommSemigroup.toAddCommMagma.{u_1} R (AddCommMonoid.toAddCommSemigroup.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.3))) (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.15 : Archimedean.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.6] {r : R}, (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddCommMonoid.toAddMonoid.{u_1} R inst._@.Mathlib.Algebra.Order.Archimedean.IndicatorCard.759627203._hygCtx._hyg.3)))))) r) -> (forall {s : Set.{0} Nat}, Iff (Set.Infinite.{0} Nat s) (Filter.Tendsto.{0, u_1} Nat R (fun (n : Nat) => Finset.sum.{0, u_1} Nat R 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Group.Multiset.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.GroupWithZero.Action.Synonym.sym.json

@@ -0,0 +1 @@
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