reserve i for object;
reserve S for non empty ManySortedSign;
reserve D for non empty set,
  n for Nat;

theorem Th5:
  for S being non empty ManySortedSign st S is trivial for A being
  MSAlgebra over S, c1,c2 being Component of the Sorts of A holds c1 = c2
proof
  let S be non empty ManySortedSign such that
A1: S is trivial;
  let A be MSAlgebra over S, c1,c2 be Component of the Sorts of A;
 (ex i1 being object st i1 in the carrier of S & c1 = (the Sorts of A).i1 )&
ex i2 being object st i2 in the carrier of S & c2 = (the Sorts of A).i2
by
PBOOLE:138;
  hence thesis by A1;
end;
