reserve x,y,z,r,s for ExtReal;
reserve A,B for ext-real-membered set;
reserve A,B for ext-real-membered set;

theorem Th88:
  (for x,y,r st x in A & y in A & x <= r & r <= y holds r in A)
  implies A is interval
proof
  assume for x,y,r st x in A & y in A & x <= r & r <= y holds r in A;
  then for x,y,r st x in A & y in A & x < r & r < y holds r in A;
  hence thesis by Th84;
end;
