reserve A,X for non empty set;
reserve f for PartFunc of [:X,X:],REAL;
reserve a for Real;

theorem Th5:
  for X being set, R being Relation of X st X c= field R
  holds R[*] is_reflexive_in X
  proof
    let X be set, R be Relation of X such that
A1: X c= field R;
    let x be object;
    assume
A2: x in X;
    set p = <*x*>;
A3: len p = 1 by FINSEQ_1:40;
    then
A4: p.(len p) = x;
    for i being Nat st i >= 1 & i < len p holds [p.i,p.(i+1)] in R
    by FINSEQ_1:40;
    hence [x,x] in R[*] by A1,A2,A3,A4,FINSEQ_1:def 17;
  end;  
