
theorem
  for f being FinSequence, k2 being Nat holds smid(f,0,k2)=smid(f,1,k2+1)
proof
  let f be FinSequence, k2 be Nat;
  thus smid(f,0,k2)=(f/^0)|(k2+1-'0) by NAT_2:8
    .= f|(k2+1-'0) by FINSEQ_5:28
    .= f|(k2+1) by NAT_D:40
    .= f|(k2+1+1-'1) by NAT_D:34
    .= (f/^0)|(k2+1+1-'1) by FINSEQ_5:28
    .= smid(f,1,k2+1) by NAT_2:8;
end;
