声明
banach_fixed_point_from_args
Mathlib.Analysis.FixedPoint.Banach
包
2
模块
63
定理
750
声明
1016
非可信 sidecar
源文本和展示 overlay 属于展示元数据。可信证据是签名证书和 checker 结果。
陈述
forall (Scalar : Sort u), forall (zero : Scalar), forall (one : Scalar), forall (add : forall (a : Scalar), forall (b : Scalar), Scalar), forall (neg : forall (a : Scalar), Scalar), forall (sub : forall (a : Scalar), forall (b : Scalar), Scalar), forall (mul : forall (a : Scalar), forall (b : Scalar), Scalar), forall (le_rel : forall (a : Scalar), forall (b : Scalar), Prop), forall (Vector : Sort v), forall (vzero : Vector), forall (vadd : forall (x : Vector), forall (y : Vector), Vector), forall (vneg : forall (x : Vector), Vector), forall (smul : forall (a : Scalar), forall (x : Vector), Vector), forall (norm : forall (x : Vector), Scalar), forall (domain : forall (x : Vector), Prop), forall (T : forall (x : Vector), Vector), forall (CauchySmall : forall (Sequence : Sort s), forall (seq : forall (n : Sequence), Vector), forall (eps : Scalar), Prop), forall (ConvergesSmall : forall (Sequence : Sort s), forall (seq : forall (n : Sequence), Vector), forall (limit : Vector), forall (eps : Scalar), Prop), forall (k : Scalar), forall (stable : forall (x : Vector), Prop), forall (args : @BanachFixedPointArgs.{s,u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T CauchySmall ConvergesSmall k stable), forall (complete_args : @CompleteMetricArgs.{s,u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm CauchySmall ConvergesSmall), forall (strict_k : Prop), forall (strict_k_holds : strict_k), forall (self_map : @SelfMapOn.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T), forall (contractive : @ContractiveOn.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T k), @FixedPointResult.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T stable
证明项
fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun Vector => fun vzero => fun vadd => fun vneg => fun smul => fun norm => fun domain => fun T => fun CauchySmall => fun ConvergesSmall => fun k => fun stable => fun args => fun complete_args => fun strict_k => fun strict_k_holds => fun self_map => fun contractive => args complete_args strict_k strict_k_holds self_map contractive
常量
Mathlib.Analysis.FixedPoint.Banach.BanachFixedPointArgs
Interface hash: sha256:249bb14fa8e382526797abbb6bb78e8f400ef5e410068c96b2e5c22c1d8333a1
Mathlib.Analysis.FixedPoint.Banach.CompleteMetricArgs
Interface hash: sha256:02e89722507270cffacfa34964cd11a301d284b01f2436b76ff00b13434deccd
Mathlib.Analysis.FixedPoint.Banach.ContractiveOn
Interface hash: sha256:04cf8342c62bbf9ebd508b271307fba07babc4752ffd6c8320535b10c3a8ed6f
Mathlib.Analysis.FixedPoint.Banach.FixedPointResult
Interface hash: sha256:9977af85154f3be6defe40a3ab4cb87706146fe862aeeec9018c0b5eeb68f5af
Mathlib.Analysis.FixedPoint.Banach.SelfMapOn
Interface hash: sha256:61e1fe7f10d74ab89648900ae20a5605b93bf63a15ced80e1199b78f0045a5d3