:: BOOLE semantic presentation

theorem Th1: :: BOOLE:1
for X being set holds X \/ {} = X
proof end;

theorem Th2: :: BOOLE:2
for X being set holds X /\ {} = {}
proof end;

theorem Th3: :: BOOLE:3
for X being set holds X \ {} = X
proof end;

theorem Th4: :: BOOLE:4
for X being set holds {} \ X = {}
proof end;

theorem Th5: :: BOOLE:5
for X being set holds X \+\ {} = X
proof end;

theorem Th6: :: BOOLE:6
for X being set st X is empty holds
X = {} by XBOOLE_0:def 5;

theorem Th7: :: BOOLE:7
for x, X being set st x in X holds
not X is empty
proof end;

theorem Th8: :: BOOLE:8
for X, Y being set st X is empty & X <> Y holds
not Y is empty
proof end;