reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;
reserve X for non empty set,
  x for Element of X;
reserve F for Part-Family of X;

theorem Th40:
  for X being set, p being a_partition of X holds {p} is Part-Family of X
proof
  let X be set;
  let p be a_partition of X;
  for x be set st x in {p} holds x is a_partition of X by TARSKI:def 1;
  hence thesis by Def7;
end;
