reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem
 s1 | (SCM-Data-Loc \/ {IC SCMPDS})
  = s2 | (SCM-Data-Loc \/ {IC SCMPDS}) implies s1 =  s2
proof
  set Y = NAT;
  set X = SCM-Data-Loc \/ {IC SCMPDS};
A1:  s1 = s1|(Data-Locations SCMPDS \/ {IC SCMPDS})
   &  s2 = s2|(Data-Locations SCMPDS \/ {IC SCMPDS}) by MEMSTR_0:33;
  thus thesis by A1,SCMPDS_2:84;
end;
