reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;
reserve L for non empty LattStr,
  a,b,c for Element of L;
reserve L for Lattice;
reserve a,b,c,u,v for Element of L;
reserve A for non empty set,
  x for Element of A,
  B for Element of Fin A,
  f,g for Function of A, the carrier of L;

theorem Th34:
  B <> {} & f|B = g|B implies FinJoin(B,f) = FinJoin(B,g)
proof
  assume that
A1: B <> {} and
A2: f|B = g|B;
  f.:B = g.:B by A2,RELAT_1:166;
  hence thesis by A1,SETWISEO:26;
end;
