law_of_cosines_scalar_rhs_from_ring_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 (ring_args : @RingLawArgs.{u} Scalar zero one add neg sub mul), forall (a : Scalar), forall (b : Scalar), forall (x : Scalar), @Eq.{u} Scalar (add (add a (mul (@two.{u} Scalar one add) (neg x))) b) (sub (add a b) (mul (@two.{u} Scalar one add) x))

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun ring_args => fun a => fun b => fun x => @Eq.rec.{u,0} Scalar (add (add a (neg (mul (@two.{u} Scalar one add) x))) b) (fun (y : Scalar) => fun (hy : @Eq.{u} Scalar (add (add a (neg (mul (@two.{u} Scalar one add) x))) b) y) => @Eq.{u} Scalar (add (add a (mul (@two.{u} Scalar one add) (neg x))) b) y) (@Eq.rec.{u,0} Scalar (mul (@two.{u} Scalar one add) (neg x)) (fun (y : Scalar) => fun (hy : @Eq.{u} Scalar (mul (@two.{u} Scalar one add) (neg x)) y) => @Eq.{u} Scalar (add (add a (mul (@two.{u} Scalar one add) (neg x))) b) (add (add a y) b)) (@Eq.refl.{u} Scalar (add (add a (mul (@two.{u} Scalar one add) (neg x))) b)) (neg (mul (@two.{u} Scalar one add) x)) (@mul_two_neg_from_ring_args.{u} Scalar zero one add neg sub mul ring_args x)) (sub (add a b) (mul (@two.{u} Scalar one add) x)) (@add_neg_cross_term_to_sub_sum_from_ring_args.{u} Scalar zero one add neg sub mul ring_args a b (mul (@two.{u} Scalar one add) x))