theorem Th71:
  p is x-context_including implies x-context_pos_in p in dom p &
  x-context_in p = p.(x-context_pos_in p)
  proof
    assume
A0: p is x-context_including;
    then
A1: p.(x-context_pos_in p) is context of x by CPI;
    thus x-context_pos_in p in dom p by A0,CPI;
    then p.(x-context_pos_in p) in rng p by FUNCT_1:def 3;
    hence thesis by A0,A1,CIn;
  end;
