reserve x for set,
  k for Element of NAT;
reserve s for State of SCMPDS;
reserve d1,d2,d3,d4,d5 for Element of SCM-Data-Loc,
  k1,k2,k3,k4,k5,k6 for Integer;
reserve I for Instruction of SCMPDS;
reserve a,b,c for Int_position;

theorem
  for ins being Instruction of SCMPDS st InsCode ins = 10 holds ex a,b,
  k1,k2 st ins = SubFrom(a,k1,b,k2)
proof
  let I be Instruction of SCMPDS such that
A1: InsCode I = 10;
  I in {[0,{},{}]} or
  I in S1 or I in S2 or I in S3 or I in S4 or I in S5 by Lm1;
  then consider
  I1 being Element of Segm 15, d1,d2 being Element of SCM-Data-Loc,
  k1,k2 being Element of INT such that
A2: I=[I1,{},<*d1,d2,k1,k2*>]and
 I1 in {9,10,11,12,13} by A1,Lm9;
  consider d1,d2,k1,k2 such that
A3: I=[10,{},<*d1,d2,k1,k2*>] by A1,A2;
  reconsider a=d1,b=d2 as Int_position by AMI_2:def 16;
  take a,b,k1,k2;
  thus thesis by A3;
end;
