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;