reserve x,A for set, i,j,k,m,n, l, l1, l2 for Nat;
reserve D for non empty set, z for Nat;
reserve S for COM-Struct;
reserve ins for Element of the InstructionsF of S;
reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set;
reserve i, j, k for Nat,
  n for Nat,
  l,il for Nat;
reserve
  i,j,k for Instruction of S,
  I,J,K for Program of S;
reserve k1,k2 for Integer;
reserve l,l1,loc for Nat;
reserve i1,i2 for Instruction of S;
reserve
  i,j,k for Instruction of S,
  I,J,K for Program of S;
reserve m for Nat;
reserve I,J for Program of S;
reserve i for Instruction of S,
        I for Program of S;
reserve loc for Nat;

theorem Th44:
  x in dom Macro i iff x= 0 or x= 1
proof
  set si=Macro i, A = NAT;
A1: card si = 2 by Th40;
  hereby
    assume
A2: x in dom si;
    reconsider l=x as Element of NAT by A2;
    reconsider n = l as Element of NAT;
    n < 1+1 by A1,A2,AFINSQ_1:66;
    then n <= 1 by NAT_1:13;
    hence x= 0 or x= 1 by NAT_1:25;
  end;
  thus thesis by A1,AFINSQ_1:66;
end;
