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;

theorem Th6:
  for F being MacroInstruction of S st card F = 1 holds F = Stop S
proof let F be MacroInstruction of S;
  assume
A1: card F = 1;
  then consider x being object such that
A2: F = {x} by CARD_2:42;
  x in F by A2,TARSKI:def 1;
  then consider a, b being object such that
A3: [a,b] = x by RELAT_1:def 1;
A4: dom F = {a} by A2,A3,RELAT_1:9;
A5: 0 in dom F by AFINSQ_1:65;
  then
A6: a = 0 by A4;
  card F -' 1 = card F - 1 by PRE_CIRC:20
    .= 0 by A1;
  then LastLoc F = 0 by AFINSQ_1:70;
  then F.0 = halt S by Def6;
  then halt S in rng F by A5,FUNCT_1:def 3;
  then halt S in {b} by A2,A3,RELAT_1:9;
  then F = {[0,halt S]} by A2,A3,A6,TARSKI:def 1
    .= 0 .--> halt S by FUNCT_4:82;
  hence thesis;
end;
