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

theorem
  for A being Matrix of n,k,REAL, B being Matrix of k,m,REAL,C being
  Matrix of m,l,REAL st n>0 & k>0 & m>0 holds A*B*C=A*(B*C)
proof
  let A be Matrix of n,k,REAL, B be Matrix of k,m,REAL,C be Matrix of m,l,REAL;
  assume that
A1: n>0 and
A2: k>0 and
A3: m>0;
A4: width B=m & len C=m by A2,A3,MATRIX_0:23;
  width A=k & len B=k by A1,A2,MATRIX_0:23;
  hence thesis by A4,MATRIX_3:33;
end;
