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 Th10:
  m |-> (n |-> a) is Matrix of m,n,D
proof
  reconsider n1=n,m1=m as Nat;
  reconsider d= n1 |-> a as Element of D* by FINSEQ_1:def 11;
  reconsider M= m1 |-> d as FinSequence of D*;
  reconsider M as Matrix of D by Th2;
  M is (m,n)-size
  proof
    thus len M = m by CARD_1:def 7;
    let p;
A1: rng M c= {n |-> a} by FUNCOP_1:13;
    assume p in rng M;
    then p = n |-> a by A1,TARSKI:def 1;
    hence thesis by CARD_1:def 7;
  end;
  hence thesis;
end;
