theorem Th44:
  for N st N c= dom A & N is non empty holds Solutions_of(A,B) c=
  Solutions_of(Segm(A,N,Seg width A), Segm(B,N,Seg width B))
proof
  let N such that
A1: N c= dom A and
A2: N is non empty;
  rng Sgm N = N by FINSEQ_1:def 14;
  hence thesis by A1,A2,Th42;
end;
