reserve a, b, c, a1, a2, b1, b2 for Int-Location,
  l, l1, l2 for Nat,
  f, g, f1, f2 for FinSeq-Location,
  i, j for Instruction of SCM+FSA,
  X, Y for set;

theorem Th7:
  a1=0_goto l1 = a2=0_goto l2 implies a1 = a2 & l1 = l2
proof
  assume
A1: a1=0_goto l1 = a2=0_goto l2;
  consider A1 being Data-Location such
  that
A2: a1 = A1 & a1=0_goto l1 = A1=0_goto l1 by SCMFSA_2:def 14;
  consider A2 being Data-Location such
  that
A3: a2 = A2 & a2=0_goto l2 = A2=0_goto l2 by SCMFSA_2:def 14;
A4: <*l2*>.1 = l2 & <*A2*>.1 = A2;
  <*l1*>.1 = l1 & <*A1*>.1 = A1;
  hence thesis by A1,A2,A3,A4,XTUPLE_0:3;
end;
