theorem Th15:
  for D be non empty set, A be Matrix of n,m,D, B be Matrix of n,k
  ,D for i st i in Seg n holds Line(A^^B,i)=Line(A,i)^Line(B,i)
proof
  let D be non empty set, A be Matrix of n,m,D, B be Matrix of n,k,D;
  set AB=A^^B;
A1: len AB=n & dom AB=Seg len AB by FINSEQ_1:def 3,MATRIX_0:def 2;
  let i such that
A2: i in Seg n;
  Line(A,i)=A.i & Line(B,i)=B.i by A2,MATRIX_0:52;
  hence Line(A,i)^Line(B,i) = AB.i by A2,A1,PRE_POLY:def 4
    .= Line(AB,i) by A2,MATRIX_0:52;
end;
