Article HIDDEN, MML version 4.99.1005

:: HIDDEN:modenot 1 => HIDDEN:mode 1
definition
  mode set;
end;

:: HIDDEN:prednot 1 => HIDDEN:pred 1
definition
  let a1, a2 be set;
  pred a1 = a2;
  symmetry;
::  for a1, a2 being set
::        st a1 = a2
::     holds a2 = a1;
  reflexivity;
::  for a1 being set holds
::     a1 = a1;
end;

:: HIDDEN:prednot 2 => not HIDDEN:pred 1
notation
  let a1, a2 be set;
  antonym a1 <> a2 for a1 = a2;
end;

:: HIDDEN:prednot 3 => HIDDEN:pred 2
definition
  let a1, a2 be set;
  pred a1 in a2;
  asymmetry;
::  for a1, a2 being set
::        st a1 in a2
::     holds not a2 in a1;
end;