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 Th8:
  card GCD-Algorithm = 15
proof
  set GCD1=i00 ';' i01 ';' i02 ';' i03 ';' i04,
  GCD2=GCD1 ';' i05 ';' i06 ';' i07 ';' i08 ';' i09;
A1: card GCD1=card (i00 ';' i01 ';' i02 ';' i03)+ 1 by Th4
    .=card (i00 ';' i01 ';' i02)+1+1 by Th4
    .=card (i00 ';' i01)+1+1+1 by Th4
    .=2+1+1+1 by Th5
    .=5;
A2: card GCD2=card (GCD1 ';' i05 ';' i06 ';' i07 ';' i08 )+ 1 by Th4
    .=card (GCD1 ';' i05 ';' i06 ';' i07)+1+1 by Th4
    .=card (GCD1 ';' i05 ';' i06) +1+1+1 by Th4
    .=card (GCD1 ';' i05 )+1+1+1+1 by Th4
    .=5+1+1+1+1+1 by A1,Th4
    .=10;
  thus
  card GCD-Algorithm =card(GCD2 ';' i10 ';' i11 ';' i12 ';' i13)+1 by Th4
    .=card(GCD2 ';' i10 ';' i11 ';' i12)+1+1 by Th4
    .=card(GCD2 ';' i10 ';' i11)+1+1+1 by Th4
    .=card(GCD2 ';' i10)+1+1+1+1 by Th4
    .=10+1+1+1+1+1 by A2,Th4
    .=15;
end;
