reserve m,n for Nat,
  a,b for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  I,J for Program of SCMPDS;

theorem Th2:
  for s being State of SCMPDS,m1,m2 being Nat st IC s= (m1+m2)
  holds ICplusConst(s,-m2)= m1
proof
  let s be State of SCMPDS,m1,m2 be Nat;
  assume
A1: IC s= (m1+m2);
  consider m being Element of NAT such that
A2: m = IC s and
A3: ICplusConst(s,-m2) = |.m+(-m2).| by SCMPDS_2:def 18;
A4: m=m1+m2 by A1,A2
    .=(m1+m2);
  thus ICplusConst(s,-m2) =m1 by A3,A4,ABSVALUE:def 1
    .=m1
    .= m1;
end;
