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

theorem
  for cn being Real,q1,q2 being Point of TOP-REAL 2 st -1<cn & cn<1 & q1
`2<0 & q2`2<0 & q1`1/|.q1.|<q2`1/|.q2.| holds for p1,p2 being Point of TOP-REAL
2 st p1=(cn-FanMorphS).q1 & p2=(cn-FanMorphS).q2 holds p1`1/|.p1.|<p2`1/|.p2.|
proof
  let cn be Real,q1,q2 be Point of TOP-REAL 2;
  assume that
A1: -1<cn and
A2: cn<1 and
A3: q1`2<0 and
A4: q2`2<0 and
A5: q1`1/|.q1.|<q2`1/|.q2.|;
  let p1,p2 be Point of TOP-REAL 2;
  assume that
A6: p1=(cn-FanMorphS).q1 and
A7: p2=(cn-FanMorphS).q2;
  per cases;
  suppose
    q1`1/|.q1.|>=cn & q2`1/|.q2.|>=cn;
    hence thesis by A2,A3,A4,A5,A6,A7,Th139;
  end;
  suppose
    q1`1/|.q1.|>=cn & q2`1/|.q2.|<cn;
    hence thesis by A5,XXREAL_0:2;
  end;
  suppose
A8: q1`1/|.q1.|<cn & q2`1/|.q2.|>=cn;
    then p2`1>=0 by A2,A4,A7,Th137;
    then
A9: p2`1/|.p2.|>=0;
    p1`1<0 by A1,A3,A6,A8,Th138;
    hence thesis by A9,Lm1,JGRAPH_2:3,XREAL_1:141;
  end;
  suppose
    q1`1/|.q1.|<cn & q2`1/|.q2.|<cn;
    hence thesis by A1,A3,A4,A5,A6,A7,Th140;
  end;
end;
