reserve x for set,
  m,n for Nat,
  a,b for Int_position,
  i,j,k for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem Th7: ::SCMPDS_5:20
  for s being 0-started State of SCMPDS
  for I being Program of SCMPDS st I is_closed_on s,P1 &
   stop I c= P1 & stop I c= P2
  for k being Nat holds  Comput(P1,s,k)
   =  Comput(P2,s,k)
   & CurInstr(P1,Comput(P1,s,k)) = CurInstr(P2,Comput(P2,s,k))
proof
  let s be 0-started State of SCMPDS;
  let I be Program of SCMPDS;
  set iI= stop I;
  assume that
A1: I is_closed_on s,P1 and
A2: stop I c= P1 and
A3: stop I c= P2;
A4: Start-At(0,SCMPDS) c= s by MEMSTR_0:29;
A5: s = Initialize s by A4,FUNCT_4:98;
A6: P2=P2 +* iI by A3,FUNCT_4:98;
A7: DataPart s = DataPart s;
  P1=P1 +* iI by A2,FUNCT_4:98;
  hence thesis by A1,A6,A7,Th6,A5;
end;
