reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th70:
  for F being Function of [:D,D9:],E for p being FinSequence of D
for q being FinSequence of D9 st len p = len q & r = F.:(p,q) holds len r = len
  p & len r = len q
proof
  let F be Function of [:D,D9:],E;
  let p be FinSequence of D;
  let q be FinSequence of D9;
  assume that
A1: len p = len q and
A2: r = F.:(p,q);
  len r = min(len p,len q) by A2,Th69;
  hence thesis by A1;
end;
