parallelogram_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 (add a x) b) (add (sub a x) b)) (add (mul (@two.{u} Scalar one add) a) (mul (@two.{u} Scalar one add) b))

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun ring_args => fun a => fun b => fun x => @eq_calc3.{u} Scalar (add (add (add a x) b) (add (sub a x) b)) (add (add a a) (add b b)) (add (mul (@two.{u} Scalar one add) a) (add b b)) (add (mul (@two.{u} Scalar one add) a) (mul (@two.{u} Scalar one add) b)) (@add_cross_and_sub_cross_cancel_from_ring_args.{u} Scalar zero one add neg sub mul ring_args a b x) (@eq_congr2.{u,u,u} Scalar Scalar Scalar add (add a a) (mul (@two.{u} Scalar one add) a) (add b b) (add b b) (@eq_symm.{u} Scalar (mul (@two.{u} Scalar one add) a) (add a a) (@two_mul_from_ring_args.{u} Scalar zero one add neg sub mul ring_args a)) (@Eq.refl.{u} Scalar (add b b))) (@eq_congr2.{u,u,u} Scalar Scalar Scalar add (mul (@two.{u} Scalar one add) a) (mul (@two.{u} Scalar one add) a) (add b b) (mul (@two.{u} Scalar one add) b) (@Eq.refl.{u} Scalar (mul (@two.{u} Scalar one add) a)) (@eq_symm.{u} Scalar (mul (@two.{u} Scalar one add) b) (add b b) (@two_mul_from_ring_args.{u} Scalar zero one add neg sub mul ring_args b)))