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声明

fixed_point_evidence_intro

Mathlib.Analysis.FixedPoint.Banach

2

模块

63

定理

750

声明

1016

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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 (fixed : Vector), forall (stable : forall (x : Vector), Prop), forall (point_mem_law : domain fixed), forall (fixed_law : @FixedPoint.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T fixed), forall (unique_law : forall (other : Vector), forall (other_mem : domain other), forall (other_fixed : @FixedPoint.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T other), @Eq.{v} Vector other fixed), forall (stable_law : @FixedPointStability.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T stable), @FixedPointEvidence.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T fixed 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 fixed => fun stable => fun point_mem_law => fun fixed_law => fun unique_law => fun stable_law => fun (P : Prop) => fun (mk : forall (point_mem_law : domain fixed), forall (fixed_law : @FixedPoint.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T fixed), forall (unique_law : forall (other : Vector), forall (other_mem : domain other), forall (other_fixed : @FixedPoint.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T other), @Eq.{v} Vector other fixed), forall (stable_law : @FixedPointStability.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T stable), P) => mk point_mem_law fixed_law unique_law stable_law

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