right_triangle_neg_left_dot_zero_from_rt

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 (ring_args : @RingLawArgs.{u} Scalar zero one add neg sub mul), forall (inner_args : @InnerProductLawArgs.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner), forall (A : PointCarrier), forall (B : PointCarrier), forall (C : PointCarrier), forall (h : @RightTriangle.{p,u,v} Scalar zero Vector inner PointCarrier disp_op A B C), @Eq.{u} Scalar (@dot.{u,v} Scalar Vector inner (vneg (@disp.{p,v} PointCarrier Vector disp_op A B)) (@disp.{p,v} PointCarrier Vector disp_op A C)) zero

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 ring_args => fun inner_args => fun A => fun B => fun C => fun h => @Eq.rec.{u,0} Scalar (neg zero) (fun (z : Scalar) => fun (hz : @Eq.{u} Scalar (neg zero) z) => @Eq.{u} Scalar (@dot.{u,v} Scalar Vector inner (vneg (@disp.{p,v} PointCarrier Vector disp_op A B)) (@disp.{p,v} PointCarrier Vector disp_op A C)) z) (@Eq.rec.{u,0} Scalar (neg (@dot.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C))) (fun (z : Scalar) => fun (hz : @Eq.{u} Scalar (neg (@dot.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C))) z) => @Eq.{u} Scalar (@dot.{u,v} Scalar Vector inner (vneg (@disp.{p,v} PointCarrier Vector disp_op A B)) (@disp.{p,v} PointCarrier Vector disp_op A C)) z) (@dot_neg_left_from_inner_args.{u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner inner_args (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C)) (neg zero) (@Eq.rec.{u,0} Scalar (@dot.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C)) (fun (q : Scalar) => fun (hq : @Eq.{u} Scalar (@dot.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C)) q) => @Eq.{u} Scalar (neg (@dot.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C))) (neg q)) (@Eq.refl.{u} Scalar (neg (@dot.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op A C)))) zero (@right_triangle_legs_dot_zero_from_rt.{p,u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner PointCarrier disp_op A B C h))) zero (@neg_zero_from_ring_args.{u} Scalar zero one add neg sub mul ring_args)