theorem
  for B st x in conv I & for y st y in B holds (x|--I).y = 0
    holds x in conv (I\B)
 proof
  let B such that
   A1: x in conv I and
   A2: for y st y in B holds(x|--I).y=0;
  set IB=I\B;
  A3: conv I c=Affin I by Th65;
  then x|--I=x|--IB by A1,A2,Th75;
  then A4: for v st v in IB holds 0<=(x|--IB).v by A1,Th71;
  A5: IB is affinely-independent by Th43,XBOOLE_1:36;
  x in Affin IB by A1,A2,A3,Th75;
  hence thesis by A4,A5,Th73;
 end;
