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

theorem
  Base_FinSeq(1,1)= <* 1 *> & Base_FinSeq(2,1)= <* 1,0 *> & Base_FinSeq(
2,2)= <* 0,1 *> & Base_FinSeq(3,1)= <* 1,0,0 *> & Base_FinSeq(3,2)= <* 0,1,0 *>
  & Base_FinSeq(3,3)= <* 0,0,1 *>
proof
  thus Base_FinSeq(1,1) = Replace (<*In(0,REAL)*>,1,In(1,REAL))
     by FINSEQ_2:59
    .= <* 1 *> by FINSEQ_7:12;
  thus Base_FinSeq(2,1)
    = Replace (<* In(0,REAL),In(0,REAL)*>,1,In(1,REAL))
        by FINSEQ_2:61
    .= <* 1,0 *> by FINSEQ_7:13;
  thus Base_FinSeq(2,2) = Replace (<* In(0,REAL),In(0,REAL) *>,2,In(1,REAL))
    by FINSEQ_2:61
    .= <* 0,1 *> by FINSEQ_7:14;
  thus Base_FinSeq(3,1) = Replace (<* 0,0,0 *>,1,In(1,REAL)) by FINSEQ_2:62
    .= <* 1,0,0 *> by FINSEQ_7:15;
  thus Base_FinSeq(3,2) =
    Replace (<* In(0,REAL),In(0,REAL), In(0,REAL )*>,2,In(1,REAL))
                by FINSEQ_2:62
    .= <* 0,1,0 *> by FINSEQ_7:16;
  thus Base_FinSeq(3,3)
  = Replace (<* In(0,REAL),In(0,REAL), In(0,REAL) *>,3,In(1,REAL))
     by FINSEQ_2:62
    .= <* 0,0,1 *> by FINSEQ_7:17;
end;
