reserve S,S9 for non void Signature,
  f,g for Function;

theorem Th61:
  for S being non void Signature for A being disjoint_valued
  MSAlgebra over S for C1,C2 being Component of the Sorts of A holds C1 = C2 or
  C1 misses C2
proof
  let S be non void Signature;
  let A be disjoint_valued MSAlgebra over S;
  let C1,C2 be Component of the Sorts of A;
A1: ex y being object st y in dom the Sorts of A & C2 = (the Sorts of A).y
  by FUNCT_1:def 3;
A2: the Sorts of A is disjoint_valued by MSAFREE1:def 2;
  ex x being object st x in dom the Sorts of A & C1 = (the Sorts of A).x
  by FUNCT_1:def 3;
  hence thesis by A1,A2,PROB_2:def 2;
end;
