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 Th14:
  for S being COM-Struct, F, G being Program of S
  holds (F ';' G).LastLoc F = IncAddr(G,card F -' 1).0
proof
  let S be COM-Struct, F, G be Program of S;
  set k = card F -' 1;
A1: LastLoc F = (0 qua Nat)+k by AFINSQ_1:70;
A2: 0 in dom IncAddr(G,k) by AFINSQ_1:65;
  dom Reloc(G,k) = {(m+k) where m is Nat: m in dom IncAddr(G,k)}
  by VALUED_1:def 12;
  then LastLoc F in dom Reloc(G,k) by A1,A2;
  hence (F ';' G).LastLoc F = (Reloc(G,k)).LastLoc F by FUNCT_4:13
    .= IncAddr(G,k).0 by A1,A2,VALUED_1:def 12;
end;
