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 k1 be Integer,s1,s2 being State of SCMPDS st IC s1 = IC s2
  holds ICplusConst(s1,k1)=ICplusConst(s2,k1)
proof
  let k1 be Integer,s1,s2 be State of SCMPDS;
A1: ex i being Element of NAT st i = IC s1 & ICplusConst(s1,k1 ) = |.i+k1.|
  by SCMPDS_2:def 18;
  assume IC s1 = IC s2;
  hence thesis by A1,SCMPDS_2:def 18;
end;
