theorem Th50:
  for r being Real holds r*|[ x,y,z ]| = |[ r*x, r*y, r*z ]|
proof
  let r be Real;
  set p = |[ x,y,z ]|;
  r*p = |[ r*p.1, r*p.2, r*p.3 ]| by Th49
    .=|[ r*x, r*p.2, r*p.3 ]|
    .=|[ r*x, r*y, r*p.3 ]|
    .=|[ r*x, r*y, r*z ]|;
    hence thesis;
end;
