reserve X for set,
  Y for non empty set;
reserve n for Nat;
reserve r for Real,
  M for non empty MetrSpace;
reserve n for Nat,
  p,q,q1,q2 for Point of TOP-REAL 2,
  r,s1,s2,t1,t2 for Real,
  x,y for Point of Euclid 2;

theorem Th26:
  dist(r*p,r*q) = |.r.|*dist(p,q)
proof
  thus dist(r*p,r*q) = dist(r*p-r*p,r*p-r*q) by Th25
    .= dist(|[0,0]|,r*p-r*q) by EUCLID:54,RLVECT_1:5
    .= dist(|[0,0]|,r*(p-q)) by RLVECT_1:34
    .= |.r.|*dist(|[0,0]|,p-q) by Th20
    .= |.r.|*dist(p-p,p-q) by EUCLID:54,RLVECT_1:5
    .= |.r.|*dist(p,q) by Th25;
end;
