reserve k for Nat;

theorem Th15:
  for n be Nat st n >= 1 holds for m,k be Nat st m
  is_represented_by n,k holds m = SDDec2(DecSD2(m,n,k),k)
proof
  let n be Nat;
  assume
A1: n >= 1;
  let m,k be Nat;
  assume
A2: m is_represented_by n,k;
  SDDec2(DecSD2(m,n,k),k) = SDDec(DecSD(m,n,k)) by Th13,Th14;
  hence thesis by A1,A2,RADIX_1:22;
end;
