hypotenuse_vector_eq_sub_legs_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 (inner : forall (x : Vector), forall (y : Vector), Scalar), forall (PointCarrier : Sort p), forall (disp_op : forall (A : PointCarrier), forall (B : PointCarrier), Vector), forall (vector_args : @VectorSpaceLawArgs.{u,v} Scalar zero one add neg sub mul Vector vzero vadd vneg smul), forall (affine_args : @AffineLawArgs.{p,u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner PointCarrier disp_op), forall (A : PointCarrier), forall (B : PointCarrier), forall (C : PointCarrier), @Eq.{v} Vector (@disp.{p,v} PointCarrier Vector disp_op B C) (@vsub.{v} Vector vadd vneg (@disp.{p,v} PointCarrier Vector disp_op A C) (@disp.{p,v} PointCarrier Vector disp_op A B))

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 inner => fun PointCarrier => fun disp_op => fun vector_args => fun affine_args => fun A => fun B => fun C => @Eq.rec.{v,0} Vector (vadd (vneg (@disp.{p,v} PointCarrier Vector disp_op A B)) (@disp.{p,v} PointCarrier Vector disp_op A C)) (fun (z : Vector) => fun (hz : @Eq.{v} Vector (vadd (vneg (@disp.{p,v} PointCarrier Vector disp_op A B)) (@disp.{p,v} PointCarrier Vector disp_op A C)) z) => @Eq.{v} Vector (@disp.{p,v} PointCarrier Vector disp_op B C) z) (@hypotenuse_vector_eq_neg_left_add_right_from_args.{p,u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner PointCarrier disp_op affine_args A B C) (@vsub.{v} Vector vadd vneg (@disp.{p,v} PointCarrier Vector disp_op A C) (@disp.{p,v} PointCarrier Vector disp_op A B)) (@vec_add_comm_from_vector_args.{u,v} Scalar zero one add neg sub mul Vector vzero vadd vneg smul vector_args (vneg (@disp.{p,v} PointCarrier Vector disp_op A B)) (@disp.{p,v} PointCarrier Vector disp_op A C))