reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th34:
  for p1,p2,p3 being FinSequence of D st len p1 = n & len p2 = n &
  len p3 = n holds <*p1,p2,p3*> is Matrix of 3,n,D
proof
  let p1,p2,p3 be FinSequence of D;
  reconsider q1 = p1,q2 = p2,q3=p3 as Element of D* by FINSEQ_1:def 11;
  reconsider M = <*q1,q2,q3*> as FinSequence of D*;
  assume
A1: len p1 =n & len p2 =n & len p3 =n;
  then reconsider M as Matrix of D by Th33;
  M is (3,n)-size
  proof
    thus len M = 3 by FINSEQ_1:45;
    let r be FinSequence of D;
    assume r in rng M;
    then r in { p1,p2,p3 } by FINSEQ_2:128;
    hence thesis by A1,ENUMSET1:def 1;
  end;
  hence thesis;
end;
