reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;
reserve r1,r2,s1,s2 for Real;

theorem Th85:
  dist(p,q) = sqrt ((p`1-q`1)^2 + (p`2-q`2)^2)
proof
A1: p = |[p`1, p`2]| by EUCLID:53;
A2: q = |[q`1, q`2]| by EUCLID:53;
  ex a, b being Point of Euclid 2 st p = a & q = b & dist(a,b) = dist(p,q)
  by Def1;
  hence thesis by A1,A2,Th84;
end;
