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 Th10:
  (f1, a1):=b1 = (f2, a2):=b2 implies a1 = a2 & b1 = b2 & f1 = f2
proof
A1: <*b1,f1,a1*>.1 = b1 & <*b1,f1,a1*>.2 = f1;
A2: <*b1,f1,a1*>.3 = a1 & <*b2,f2,a2*>.1 = b2;
A3: <*b2,f2,a2*>.2 = f2 & <*b2,f2,a2*>.3 = a2;
  assume (f1, a1):=b1 = (f2, a2):=b2;
  hence thesis by A1,A2,A3,XTUPLE_0:3;
end;
