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Declaration
fixed_point_stability_from_evidence
Mathlib.Analysis.FixedPoint.Banach
Packages
2
Module
63
Theorems
750
Declarations
1016
Untrusted sidecar
Source text and display overlays are presentation metadata. The signed certificate and checker result are the trusted evidence.
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 (fixed : Vector), forall (stable : forall (x : Vector), Prop), forall (evidence : @FixedPointEvidence.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T fixed stable), @FixedPointStability.{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 fixed => fun stable => fun evidence => evidence (@FixedPointStability.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T stable) (fun (point_mem_arg : domain fixed) => fun (fixed_eq_arg : @FixedPoint.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T fixed) => fun (unique_arg : 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) => fun (stable_arg : @FixedPointStability.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm domain T stable) => stable_arg)