reserve j, k, m, n for Nat,
  a,b for Int_position,
  k1,k2 for Integer;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

theorem
  for s1,s2 being State of SCMPDS,k1,k2 be Nat st IC s1
  = IC s2 & k1 <> k2 holds ICplusConst(s1,k1) <> ICplusConst(s2,k2)
proof
  let s1,s2 be State of SCMPDS,k1,k2 be Nat;
  reconsider m=IC s1 as Element of NAT;
  set mm=m+2;
A1: mm-2+k1>=0;
A2: mm-2+k2>=0;
  assume IC s1 = IC s2 & k1<>k2;
  hence thesis by A1,A2,Th7;
end;
