theorem Th30:
  i in Seg m & j in Seg m & mt.i = mt.j & i<>j implies Det Segm(M,
  mt1,mt) = 0.K
proof
  assume that
A1: i in Seg m and
A2: j in Seg m and
A3: mt.i = mt.j and
A4: i<>j;
A5: i<j or j<i by A4,XXREAL_0:1;
  set S = Segm(M,mt1,mt);
A6: width S=m by MATRIX_0:24;
  then
A7: Col(S,j)=Line(S@,j) by A2,MATRIX_0:59;
  Col(S,i)=Line(S@,i) by A1,A6,MATRIX_0:59;
  hence 0.K = Det (S@) by A1,A2,A3,A7,A5,Th29,MATRIX11:50
    .= Det S by MATRIXR2:43;
end;
