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;
