reserve F for total
  NAT-defined (the InstructionsF of SCM)-valued Function;

theorem Th7:
  for k, n being Element of NAT, s being State of SCM, a, b being
  Data-Location st IC Comput(F,s,k) = n & F.n = MultBy(a,b) holds
IC
  Comput(F,s,k+1) = (n+1) & Comput(F,s,k+1).a =
Comput(F,s,k).a*
Comput(F,s,k).b & for d being Data-Location st d <> a holds Comput
(F,s,k+
  1).d = Comput(F,s,k).d
proof
  let k, n be Element of NAT, s be State of SCM, a, b be Data-Location;
  assume
A1: IC Comput(F,s,k) = n;
  assume
 F.n = MultBy(a,b);
  then Comput(F,s,k+1)
   = Exec(MultBy(a,b), Comput(F,s,k)) by A1,Lm2;
  hence thesis by A1,AMI_3:5;
end;
