reserve l, m, n for Nat,
  i,j,k for Instruction of SCM+FSA,
  I,J,K for Program of SCM+FSA;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;

theorem Th11:
  card(I ";" J) = card I + card J
proof
A1: card dom(I ";" J) = card(I ";" J) & card dom I = card I;
A2: card stop Directed I = card stop I by Lm2;
  card stop I -' 1 = card I by COMPOS_1:71;
  then
A3: dom(I ";" J) = dom Directed I \/ dom Reloc(J, card I) by FUNCT_4:def 1,A2
    .= dom I \/ dom Reloc(J, card I) by FUNCT_4:99;
  card dom Reloc(J, card I) = card Reloc(J, card I) by CARD_1:62
    .= card J by COMPOS_1:49
    .= card dom J;
  hence thesis by A1,A3,CARD_2:40,COMPOS_1:48;
end;
