theorem
  for f1,i1,i2 st 1<=i2 & i2<=i1 & i1<=len f1 holds
    len mid(f1,i2, i1)=i1-'i2+1
proof
  let f1,i1,i2;
  assume that
A1: 1<= i2 and
A2: i2<=i1 and
A3: i1<= len f1;
A4: i2<=len f1 by A2,A3,XXREAL_0:2;
  1<=i1 by A1,A2,XXREAL_0:2;
  hence thesis by A1,A2,A3,A4,Th117;
end;
