reserve A,B,C,Y,x,y,z for set, U, D for non empty set,
X for non empty Subset of D, d,d1,d2 for Element of D;
reserve P,Q,R for Relation, g for Function, p,q for FinSequence;
reserve f for BinOp of D, i,m,n for Nat;

theorem Th5: for x being set holds ::#th5 1, to be replaced by Th30
(x is non empty FinSequence of D iff x in D*\{{}})
proof
let x be set;
thus x is non empty FinSequence of D implies x in D*\{{}}
proof
assume x is non empty FinSequence of D;
then not x in {{}} & x in D* by FINSEQ_1:def 11, TARSKI:def 1;
hence thesis by XBOOLE_0:def 5;
end;
assume x in D*\{{}}; then
x in D* & not x in {{}} by XBOOLE_0:def 5;
hence thesis by FINSEQ_1:def 11, TARSKI:def 1;
end;
