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;
