reserve m,n for Nat,
  a for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1 for Integer,
  loc for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

theorem Th4:
  for s being State of SCMPDS,m1,m2 being Nat st IC s=
   m1 holds ICplusConst(s,m2)= m1+m2
proof
  let s be State of SCMPDS,m1,m2 be Nat;
   ex m being Element of NAT st m = IC s & ICplusConst(s,m2) = |.m+m2.|
     by SCMPDS_2:def 18;
  hence thesis by ABSVALUE:def 1;
end;
