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;
reserve k for Nat, G for Matrix of D;
reserve x,y,x1,x2,y1,y2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  s,s2 for FinSequence,
  a,b,c,d for Element of D,
  q,r for FinSequence of D,
  a9,b9 for Element of D;

theorem
  for M1,M2 being Matrix of D st width M1>0 & width M2>0 & M1@=M2@ holds M1=M2
proof
  let M1,M2 be Matrix of D;
  assume width M1>0 & width M2>0;
  then
A1: width (M1@)=len M1 & width (M2@)=len M2 by Th54;
  assume M1@=M2@;
  hence thesis by A1,Th53;
end;
