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 Th9:
  for s being State of SCMPDS holds IC s + 1 = ICplusConst(s,1)
proof
  let s be State of SCMPDS;
  consider j being Element of NAT such that
A1: j = IC s and
A2: ICplusConst(s,1)=|.j+1.| by SCMPDS_2:def 18;
  reconsider mj = IC s as Element of NAT;
A3: j*1 >= 0;
  IC s + 1 = |.mj.|+1 by ABSVALUE:def 1
    .= |.mj.|+|.1.| by ABSVALUE:def 1
    .= |.mj+1.| by A1,A3,ABSVALUE:11;
  hence thesis by A1,A2;
end;
