reserve r, r1, r2, x, y, z,
        x1, x2, x3, y1, y2, y3 for Real;
reserve R, R1, R2, R3 for Element of 3-tuples_on REAL;
reserve p, q, p1, p2, p3, q1, q2 for Element of REAL 3;
reserve f1, f2, f3, g1, g2, g3, h1, h2, h3 for PartFunc of REAL,REAL;
reserve t, t0, t1, t2 for Real;

theorem Th78:
  (p1+p2)<X>p3 = (p1<X>p3)+(p2<X>p3)
proof
  (p1+p2)<X>p3 = -(p3<X>(p1+p2)) by Th74
   .= -((p3<X>p1)+(p3<X>p2)) by Th77
   .= -((p3<X>p1)-(p2<X>p3)) by Th74
   .= -(p3<X>p1)+(p2<X>p3) by RVSUM_1:36;
  hence thesis by Th74;
end;
