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Declaration

banach_fixed_point_from_args

Mathlib.Analysis.FixedPoint.Banach

Packages

2

Module

63

Theorems

750

Declarations

1016

Untrusted sidecar

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Statement

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

Proof term

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

Constants