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;
reserve M,M1,M2 for Matrix of D;
reserve f for FinSequence of D;
reserve i,j,i1,j1 for Nat;

theorem
 for M being Matrix of D st 1 <= i & i <= len M & 1 <= j & j <= width M
holds M*(i,j) in Values M
proof
  let M be Matrix of D;
  assume 1 <= i & i <= len M & 1 <= j & j <= width M;
  then
A1: [i,j] in Indices M by Th30;
  Values M = { M*(i1,j1) where i1,j1 is Nat
     : [i1,j1] in Indices M } by Th39;
  hence thesis by A1;
end;
