reserve i,j,k for Nat;
reserve I,J,K for Element of Segm 9,
  a,a1,a2 for Nat,
  b,b1,b2,c,c1 for Element of SCM-Data-Loc;
reserve T for InsType of SCM-Instr,
        I for Element of SCM-Instr;
reserve a,b,c for Data-Location,
  loc for Nat,
  I for Instruction of SCM;
reserve s for State of SCM;
reserve Y,K,T for Element of Segm 9,
  a1,a2,a3 for Nat,
  b1,b2,c1,c2,
  c3 for Element of SCM-Data-Loc;
reserve i,j,k for Nat;

theorem
  for I being set holds I is Instruction of SCM iff I = [0,{},{}] or (ex a,
b st I = a:=b) or (ex a,b st I = AddTo(a,b)) or (ex a,b st I = SubFrom(a,b)) or
  (ex a,b st I = MultBy(a,b)) or (ex a,b st I = Divide(a,b)) or (ex loc st I =
SCM-goto loc) or (ex a,loc st I = a=0_goto loc) or
 ex a,loc st I = a>0_goto loc by Lm12;
