reserve n for Nat;
reserve K for Field;
reserve a,b,c,d,e,f,g,h,i,a1,b1,c1,d1,e1,f1,g1,h1,i1 for Element of K;
reserve M,N for Matrix of 3,K;
reserve p for FinSequence of REAL;

theorem Th02:
  <* <* a,b,c *>,
     <* d,e,f *>,
     <* g,h,i *> *> =
  <* <* a1,b1,c1 *>,
     <* d1,e1,f1 *>,
     <* g1,h1,i1 *> *>
  implies
  a = a1 & b = b1 & c = c1 &
        d = d1 & e = e1 & f = f1 &
        g = g1 & h = h1 & i = i1
  proof
    assume <* <* a,b,c *>,
              <* d,e,f *>,
              <* g,h,i *> *> =
      <* <* a1,b1,c1 *>,
         <* d1,e1,f1 *>,
         <* g1,h1,i1 *> *>;
    then <*a,b,c*> = <*a1,b1,c1*> &
         <*d,e,f*> = <*d1,e1,f1*> &
         <*g,h,i*> = <*g1,h1,i1*> by FINSEQ_1:78;
    hence thesis by FINSEQ_1:78;
  end;
