reserve k,m,n for Nat,
  i1,i2,i3 for Integer,
  e for set;
reserve i,k,m,n,p,x,y for Nat;
reserve a for Tuple of n,(k-SD);

theorem Th22:
  m is_represented_by 1,k & n is_represented_by 1,k implies
  SD_Add_Carry(DigA(DecSD(m,1,k),1)+DigA(DecSD(n,1,k),1)) = SD_Add_Carry(m+n)
proof
  assume that
A1: m is_represented_by 1,k and
A2: n is_represented_by 1,k;
  SD_Add_Carry(DigA(DecSD(m,1,k),1)+DigA(DecSD(n,1,k),1)) = SD_Add_Carry(m
  + DigA(DecSD(n,1,k),1)) by A1,Th20
    .= SD_Add_Carry(m + n) by A2,Th20;
  hence thesis;
end;
