norm_dist_symm_from_args

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 (norm_args : @NormedSpaceLawArgs.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul norm), 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)

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 norm_args => fun x => fun y => norm_args (@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)) (fun (norm_nonneg_arg : forall (x : Vector), le_rel zero (norm x)) => fun (norm_zero_arg : @Eq.{u} Scalar (norm vzero) zero) => fun (norm_triangle_arg : forall (x : Vector), forall (y : Vector), le_rel (norm (vadd x y)) (add (norm x) (norm y))) => fun (norm_neg_arg : forall (x : Vector), @Eq.{u} Scalar (norm (vneg x)) (norm x)) => fun (norm_dist_self_arg : 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) => fun (norm_dist_symm_arg : 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)) => fun (norm_dist_triangle_arg : 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))) => norm_dist_symm_arg x y)