reserve p,p1,p2,p3,q,q1,q2 for Point of TOP-REAL 2,
  i for Nat,
  lambda for Real;

theorem Th14:
  for f,g being Function of I[01],TOP-REAL 2,
  C0,KXP,KXN,KYP,KYN being Subset of TOP-REAL 2,
  O,I being Point of I[01] st O=0 & I=1 & f is continuous one-to-one &
  g is continuous one-to-one & C0={p: |.p.|<=1}&
  KXP={q1 where q1 is Point of TOP-REAL 2:
  |.q1.|=1 & q1`2<=q1`1 & q1`2>=-q1`1} &
  KXN={q2 where q2 is Point of TOP-REAL 2:
  |.q2.|=1 & q2`2>=q2`1 & q2`2<=-q2`1} &
  KYP={q3 where q3 is Point of TOP-REAL 2:
  |.q3.|=1 & q3`2>=q3`1 & q3`2>=-q3`1} &
  KYN={q4 where q4 is Point of TOP-REAL 2:
  |.q4.|=1 & q4`2<=q4`1 & q4`2<=-q4`1} & f.O in KXP & f.I in KXN &
  g.O in KYP & g.I in KYN & rng f c= C0 & rng g c= C0 holds rng f meets rng g
proof
  let f,g be Function of I[01],TOP-REAL 2,
  C0,KXP,KXN,KYP,KYN be Subset of TOP-REAL 2, O,I be Point of I[01];
  assume
A1: O=0 & I=1 & f is continuous & f is one-to-one &
  g is continuous & g is one-to-one & C0={p: |.p.|<=1}&
  KXP={q1 where q1 is Point of TOP-REAL 2:
  |.q1.|=1 & q1`2<=q1`1 & q1`2>=-q1`1} &
  KXN={q2 where q2 is Point of TOP-REAL 2:
  |.q2.|=1 & q2`2>=q2`1 & q2`2<=-q2`1} &
  KYP={q3 where q3 is Point of TOP-REAL 2:
  |.q3.|=1 & q3`2>=q3`1 & q3`2>=-q3`1} &
  KYN={q4 where q4 is Point of TOP-REAL 2:
  |.q4.|=1 & q4`2<=q4`1 & q4`2<=-q4`1} & f.O in KXP & f.I in KXN &
  g.O in KYP & g.I in KYN & rng f c= C0 & rng g c= C0;
  then ex f2 being Function of I[01],TOP-REAL 2 st ( f2.0=f.1)&( f2
  .1=f.0)&( rng f2=rng f)&( f2 is continuous)&( f2 is one-to-one) by
JGRAPH_5:12;
  hence thesis by A1,JGRAPH_5:13;
end;
