theorem
  not o,p,c are_collinear & o,p,b are_collinear & qtrap o,p implies ex d
  st trap p,b,c,d,o
proof
  assume that
A1: ( not o,p,c are_collinear)& o,p,b are_collinear and
A2: qtrap o,p;
  consider d such that
A3: o,p,b are_collinear implies o,c,d are_collinear & p,c // b,d by A2;
  take d;
  thus thesis by A1,A3;
end;
