reserve p,q for Point of TOP-REAL 2;

theorem
  for cn being Real,q being Point of TOP-REAL 2 st -1<cn & cn<1 & q`2>=0
  holds for p being Point of TOP-REAL 2 st p=(cn-FanMorphN).q holds p`2>=0
proof
  let cn be Real,q be Point of TOP-REAL 2;
  assume that
A1: -1<cn & cn<1 and
A2: q`2>=0;
  now
    per cases by A2;
    case
      q`2>0;
      hence thesis by A1,Th18;
    end;
    case
      q`2=0;
      hence thesis by JGRAPH_4:49;
    end;
  end;
  hence thesis;
end;
