theorem Th2:
  for I,J being FinSequence-membered set, p,q being FinSequence
  st len p = len q & p <> q holds p^^I misses q^^J
  proof
    let I,J be FinSequence-membered set;
    let p,q be FinSequence;
    assume Z0: len p = len q;
    assume Z1: p <> q;
    assume p^^I meets q^^J;
    then consider a being object such that
A1: a in p^^I & a in q^^J by XBOOLE_0:3;
    consider p1 being Element of I such that
A2: a = p^p1 & p1 in I by A1;
    consider q1 being Element of J such that
A3: a = q^q1 & q1 in J by A1;
    dom p = Seg len p & dom q = Seg len q by FINSEQ_1:def 3;
    then p = (p^p1)|dom p = q by A2,A3,Z0,FINSEQ_1:21;
    hence thesis by Z1;
  end;
