theorem Th49:
  for r being Real holds r*p = |[ r*p.1, r*p.2, r*p.3 ]|
proof
    let r be Real;
A1: (r*p).1 = r*(p.1) by RVSUM_1:44;
A2: (r*p).2 = r*(p.2) by RVSUM_1:44;
    (r*p).3 = r*(p.3) by RVSUM_1:44;
    hence r*p = |[ r*p.1, r*p.2, r*p.3]| by A1,A2,Th1;
end;
