
theorem Th01:
  BK_model misses absolute
  proof
    assume not BK_model misses absolute;
    then consider x be object such that
A1: x in BK_model /\ absolute by XBOOLE_0:def 1;
A2: x in BK_model & x in absolute by A1,XBOOLE_0:def 4;
    x in {P where P is Point of ProjectiveSpace TOP-REAL 3:
    for u be Element of TOP-REAL 3 st u is non zero & P = Dir u holds
    qfconic(1,1,-1,0,0,0,u) = 0} by A2,PASCAL:def 2;
    then consider P be Point of ProjectiveSpace TOP-REAL 3 such that
A3: x = P and
A4: for u be Element of TOP-REAL 3 st u is non zero & P = Dir u holds
    qfconic(1,1,-1,0,0,0,u) = 0;
    consider u be Element of TOP-REAL 3 such that
A5: u is non zero and
A6: P = Dir u by ANPROJ_1:26;
    consider Q be Point of ProjectiveSpace TOP-REAL 3 such that
A7: x = Q and
A8: for u be Element of TOP-REAL 3 st u is non zero & Q = Dir u holds
    qfconic(1,1,-1,0,0,0,u) is negative by A2;
    qfconic(1,1,-1,0,0,0,u) = 0 &
    qfconic(1,1,-1,0,0,0,u) is negative by A3,A4,A5,A6,A7,A8;
    hence contradiction;
  end;
