reserve a,b,m,x,y,i1,i2,i3,i for Integer,
  k,p,q,n for Nat,
  c,c1,c2 for Element of NAT,
  z for set;
reserve fp,fp1 for FinSequence of NAT,

  b,c,d, n for Element of NAT,
  a for Nat;

theorem
  len fp = n+1 & a >= 1 & a <= n implies Del(fp,a).n = fp.(len fp)
proof
  assume that
A1: len fp = n+1 and
A2: a >= 1 and
A3: a <= n;
  n<n+1 by XREAL_1:29;
  then a<n+1 by A3,XXREAL_0:2;
  then a in dom fp by A1,A2,FINSEQ_3:25;
  hence thesis by A1,A3,WSIERP_1:def 1;
end;
