reserve m,n for Nat,
  a,b for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  I,J for Program of SCMPDS;

theorem Th7:
  (I ';' i ';' J). card I =i
proof
   card I in dom (I ';' i) by Th6;
  hence (I ';' i ';' J ). card I =(I ';' i). card I by AFINSQ_1:def 3
    .=i by Th6;
end;
