theorem
  A meets B implies dist(A,B) = 0
proof
  assume A meets B;
  then consider z being object such that
A1: z in A and
A2: z in B by XBOOLE_0:3;
  reconsider z as Element of COMPLEX n by A1;
  dist(z,A) = 0 & dist(z,B) = 0 by A1,A2,Th115;
  then (0 qua Nat) + (0 qua Nat) >= dist(A,B) by A1,A2,Th128;
  hence thesis by A1,A2,Th126;
end;
