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 Th8:
  for X being non empty constituted-DTrees set
  for t being DecoratedTree st t in X
  holds Subtrees t c= Subtrees X
  proof
    let X be non empty constituted-DTrees set;
    let t be DecoratedTree such that
A1: t in X;
    let x be object; assume x in Subtrees t;
    then consider p being Element of dom t such that
A2: x = t|p;
    thus thesis by A1,A2;
  end;
