reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;

theorem Th12:
  for t1,t2 being DecoratedTree st t1 in Subtrees t2
  holds Subtrees t1 c= Subtrees t2
  proof
    let t1,t2 be DecoratedTree; assume t1 in Subtrees t2;
    then consider p being Element of dom t2 such that
A1: t1 = t2|p;
    thus Subtrees t1 c= Subtrees t2 by A1,TREES_9:13;
  end;
