bounded_linear_map_bound_apply

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 (X : Sort v), forall (xzero : X), forall (xadd : forall (x : X), forall (y : X), X), forall (xneg : forall (x : X), X), forall (xsmul : forall (a : Scalar), forall (x : X), X), forall (xnorm : forall (x : X), Scalar), forall (Y : Sort w), forall (yzero : Y), forall (yadd : forall (x : Y), forall (y : Y), Y), forall (yneg : forall (y : Y), Y), forall (ysmul : forall (a : Scalar), forall (y : Y), Y), forall (ynorm : forall (y : Y), Scalar), forall (f : forall (x : X), Y), forall (bound : Scalar), forall (bounded_args : @BoundedLinearMapArgs.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f bound), forall (x : X), le_rel (ynorm (f x)) (mul bound (xnorm x))

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun X => fun xzero => fun xadd => fun xneg => fun xsmul => fun xnorm => fun Y => fun yzero => fun yadd => fun yneg => fun ysmul => fun ynorm => fun f => fun bound => fun bounded_args => fun x => bounded_args (le_rel (ynorm (f x)) (mul bound (xnorm x))) (fun (linear_arg : @LinearMapLawArgs.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f) => fun (bound_arg : @OperatorNormBound.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f bound) => bound_arg x)