reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;

theorem
  for A being RelStr, C being Chain of A, S being Subset of A holds S c=
  C implies S is Chain of A
proof
  let A be RelStr, C be Chain of A, S be Subset of A;
  assume
A1: S c= C;
  the InternalRel of A is_strongly_connected_in C by Def7;
  then the InternalRel of A is_strongly_connected_in S by A1;
  hence thesis by Def7;
end;
