reserve A for non empty set,
  S for non void non empty ManySortedSign;
reserve x for set;
reserve o for OperSymbol of S;

theorem
  for C be category st C = MSAlgCat (S,A) for o be Object of C holds o
  is strict feasible MSAlgebra over S
proof
  let C be category such that
A1: C = MSAlgCat (S,A);
  let o be Object of C;
  o in the carrier of C;
  then o in MSAlg_set (S,A) by A1,Def4;
  then ex M be strict feasible MSAlgebra over S st o = M & for C1 be Component
  of the Sorts of M holds C1 c= A by Def2;
  hence thesis;
end;
