reserve v,x for object;
reserve D,V,A for set;
reserve n for Nat;
reserve p,q for PartialPredicate of D;
reserve f,g for BinominativeFunction of D;
reserve D for non empty set;
reserve d for Element of D;
reserve f,g for BinominativeFunction of D;
reserve p,q,r,s for PartialPredicate of D;

theorem
  <*p,f,r*> is SFHT of D & <*q,f,r*> is SFHT of D implies
  <*PP_or(p,q),f,r*> is SFHT of D
  proof
    set P = PP_or(p,q);
    assume
A1: <*p,f,r*> is SFHT of D & <*q,f,r*> is SFHT of D;
    for d holds d in dom P & P.d = TRUE & d in dom f & f.d in dom r implies
     r.(f.d) = TRUE
    proof
      let d;
      assume d in dom P & P.d = TRUE;
      then d in dom p & p.d = TRUE or d in dom q & q.d = TRUE by PARTPR_1:10;
      hence thesis by A1,Th11;
    end;
    then <*P,f,r*> in SFHTs(D);
    hence thesis;
  end;
