reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;
reserve f for Function of A,B;
reserve f for Function;
reserve x1,x2,x3,x4,x5 for object;
reserve p for FinSequence;
reserve ND for non empty set;
reserve y1,y2,y3,y4,y5 for Element of ND;

theorem Th85:
  for X being non empty set, PX being a_partition of X
  for Pi being set st Pi in PX ex x being Element of X st x in Pi
proof
  let X be non empty set, PX be a_partition of X;
  let Pi be set;
  assume Pi in PX;
  then reconsider Pi as Element of PX;
  set q = the Element of Pi;
  reconsider q as Element of X;
  take q;
  thus thesis;
end;
