reserve a,b for object, I,J for set;

theorem Lem8:
  for p,q being FinSequence st p^q is I-valued
  holds p is I-valued & q is I-valued
  proof
    let p,q be FinSequence;
    assume Z1: rng (p^q) c= I;
A1: rng (p^q) = rng p \/ rng q by FINSEQ_1:31;
    rng p c= rng p \/ rng q by XBOOLE_1:7;
    hence rng p c= I by Z1,A1,XBOOLE_1:1;
    rng q c= rng p \/ rng q by XBOOLE_1:7;
    hence rng q c= I by Z1,A1,XBOOLE_1:1;
  end;
