reserve x,y for set,
  n,m for Nat,
  r,s for Real;
reserve f, g for Function;

theorem
  for f being FinSequence, k being Nat holds len (f/^k)=len f-'k
proof
  let f be FinSequence,k be Nat;
  per cases;
  suppose
A1: k<=len f;
    then len f-'k=len f-k by XREAL_1:233;
    hence thesis by A1,Def1;
  end;
  suppose
A2: k>len f;
    then (f/^k)={} by Def1;
    then
A3: len (f/^k)=0;
    len f-k<0 by A2,XREAL_1:49;
    hence thesis by A3,XREAL_0:def 2;
  end;
end;
