reserve x,y,z for object,
  i,j,n,m for Nat,
  D for non empty set,
  s,t for FinSequence,
  a,a1,a2,b1,b2,d for Element of D,
  p, p1,p2,q,r for FinSequence of D;

theorem Th12:
  for p1,p2 st len p1 =n & len p2 = n holds <*p1,p2*> is Matrix of 2,n,D
proof
  let p1,p2;
  reconsider q1 = p1,q2 = p2 as Element of D* by FINSEQ_1:def 11;
  reconsider M = <*q1,q2*> as FinSequence of D*;
  assume
A1: len p1 =n & len p2 =n;
  then reconsider M as Matrix of D by Th4;
  M is (2,n)-size
  proof
    thus len M = 2 by FINSEQ_1:44;
    let r;
    assume r in rng M;
    then r in { p1,p2 } by FINSEQ_2:127;
    hence thesis by A1,TARSKI:def 2;
  end;
  hence thesis;
end;
