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 Th24:
  dist(p,q) = dist(-p,-q)
proof
  thus dist(p,q) = dist(q-q,p-q) by Th23
    .= dist(q-q,p+-q)
    .= dist(|[0,0]|,p+-q) by EUCLID:54,RLVECT_1:5
    .= dist(p-p,p+-q) by EUCLID:54,RLVECT_1:5
    .= dist(p+-p,p+-q)
    .= dist(-p,-q) by Th21;
end;
