
theorem Th28:
  for m being Nat st m > 0 for L being non empty ZeroStr, p being
AlgSequence of L holds len mConv(p,m) = m & width mConv(p,m) = 1 & for i being
  Nat st i < m holds mConv(p,m)*(i+1,1) = p.i
proof
  let m be Nat;
  assume
A1: m > 0;
  let L be non empty ZeroStr, p be AlgSequence of L;
  set q = mConv(p,m);
  thus len q = m by A1,MATRIX_0:23;
  thus width q = 1 by A1,MATRIX_0:23;
  now
    let i be Nat;
    assume i < m;
    then 0 + 1 <= i + 1 & i+1 <= m by NAT_1:13;
    then q*(i+1,1) = p.(i+1-1) by Def3;
    hence q*(i+1,1) = p.i;
  end;
  hence thesis;
end;
