NormedSpaceLawArgs

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), Prop

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 => forall (P : Prop), forall (mk : forall (norm_nonneg_law : forall (x : Vector), le_rel zero (norm x)), forall (norm_zero_law : @Eq.{u} Scalar (norm vzero) zero), forall (norm_triangle_law : forall (x : Vector), forall (y : Vector), le_rel (norm (vadd x y)) (add (norm x) (norm y))), forall (norm_neg_law : forall (x : Vector), @Eq.{u} Scalar (norm (vneg x)) (norm x)), forall (norm_dist_self_law : forall (x : Vector), @Eq.{u} Scalar (@NormDist.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm x x) zero), forall (norm_dist_symm_law : forall (x : Vector), forall (y : Vector), @Eq.{u} Scalar (@NormDist.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm x y) (@NormDist.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm y x)), forall (norm_dist_triangle_law : forall (x : Vector), forall (y : Vector), forall (z : Vector), le_rel (@NormDist.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm x z) (add (@NormDist.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm x y) (@NormDist.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm y z))), P), P