reserve x for set,
  R for non empty Poset;
reserve S1 for OrderSortedSign,
  OU0 for OSAlgebra of S1;
reserve s,s1,s2,s3,s4 for SortSymbol of S1;

theorem Th26:
  for o be OperSymbol of S1 for A be OSSubset of OU0 for B be
OSSubset of OU0 st B in OSSubSort(A) holds ((OSMSubSort A)# * (the Arity of S1)
  ).o c= (B# * (the Arity of S1)).o
proof
  let o be OperSymbol of S1, A be OSSubset of OU0, B be OSSubset of OU0;
  assume
A1: B in OSSubSort(A);
  OSMSubSort (A) c= B
  proof
    let i be object;
    assume i in the carrier of S1;
    then reconsider s = i as SortSymbol of S1;
    (OSMSubSort A).s = meet (OSSubSort(A,s)) & B.s in (OSSubSort(A,s)) by A1
,Def10,Def11;
    hence thesis by SETFAM_1:3;
  end;
  hence thesis by MSUALG_2:2;
end;
