reserve i, j, k for Nat,
  I for Element of Segm 8,
  i1, i2 for Nat,
  d1, d2, d3, d4 for Element of SCM-Data-Loc,
  S for non empty 1-sorted;
reserve G for non empty 1-sorted;
reserve I for Element of Segm 8,
  S for non empty 1-sorted,
  t for Element of S,
  x for set,
  k for Nat;
 reserve R for Ring, T for InsType of SCM-Instr R;
reserve R for Ring,
  r for Element of R,
  a, b, c, d1, d2 for Element of SCM-Data-Loc;
reserve i1 for Nat;

theorem
  x in {1,2,3,4} implies [x,{},<*d1,d2*>] in SCM-Instr S
proof
  reconsider D1 = d1, D2 = d2 as Element of SCM-Data-Loc;
  assume
A1: x in {1,2,3,4};
  then x=1 or x=2 or x=3 or x=4 by ENUMSET1:def 2;
  then reconsider x as Element of Segm 8 by NAT_1:44;
  [x,{},<*D1,D2*>] in { [I,{},<*a,b*>]
    where a,b is Element of SCM-Data-Loc: I
  in { 1,2,3,4 } } by A1;
  then [x,{},<*D1,D2*>] in { [0,{},{}] } \/ { [I,{},<*a,b*>]
  where a,b is Element of
  SCM-Data-Loc: I in { 1,2,3,4 } } by XBOOLE_0:def 3;
  then [x,{},<*D1,D2*>] in { [0,{},{}] } \/ { [I,{},<*a,b*>]
  where a,b is Element of
SCM-Data-Loc: I in { 1,2,3,4 } } \/ the set of all  [6,<*i*>,{}]
where i is Nat by XBOOLE_0:def 3;
  then [x,{},<*D1,D2*>] in { [0,{},{}] } \/ { [I,{},<*a,b*>]
  where a,b is Element of
SCM-Data-Loc: I in { 1,2,3,4 } } \/ the set of all  [6,<*i*>,{}]
where i is Nat \/ the set of all  [7,<*i*>,<*a*>] where i is Nat,
  a is Element of
  SCM-Data-Loc by XBOOLE_0:def 3;
  hence thesis by XBOOLE_0:def 3;
end;
