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 Th11:
  <*p,f,q*> in SFHTs(D) implies
  for d holds d in dom p & p.d = TRUE & d in dom f & f.d in dom q implies
   q.(f.d) = TRUE
  proof
    assume <*p,f,q*> in SFHTs(D);
    then consider p1,q1 being PartialPredicate of D,
           f1 being BinominativeFunction of D such that
A1: <*p,f,q*> = <*p1,f1,q1*> and
A2: for d holds d in dom p1 & p1.d = TRUE & d in dom f1 & f1.d in dom q1
     implies q1.(f1.d) = TRUE;
    p = p1 & q = q1 & f = f1 by A1,FINSEQ_1:78;
    hence thesis by A2;
  end;
