reserve

  k,n,m,i,j for Element of NAT,
  K for Field;
reserve L for non empty addLoopStr;
reserve G for non empty multLoopStr;

theorem Th27:
  for i,j st 1<=i & i<=n & 1<=j & j<=n holds (1.(K,n))*(i,j)=(
  Base_FinSeq(K,n,i)).j
proof
  let i,j;
  assume that
A1: 1<=i & i<=n and
A2: 1<=j & j<=n;
  [i,j] in Indices (1.(K,n)) by A1,A2,MATRIX_0:31;
  then
  ex p3 being FinSequence of K st p3 = (1.(K,n)).i & 1.(K,n)*(i,j) = p3.j
  by MATRIX_0:def 5;
  hence thesis by A1,Th26;
end;
