let p, q be Element of LTLB_WFF ; ('not' (p '&&' q)) => (p => ('not' q)) is ctaut
let g be Function of LTLB_WFF,BOOLEAN; LTLAXIO1:def 16 (VAL g) . (('not' (p '&&' q)) => (p => ('not' q))) = 1
set v = VAL g;
A1:
(VAL g) . TFALSUM = 0
by LTLAXIO1:def 15;
A2:
( (VAL g) . p = 1 or (VAL g) . p = 0 )
by XBOOLEAN:def 3;
A3: (VAL g) . (p => ('not' q)) =
((VAL g) . p) => ((VAL g) . ('not' q))
by LTLAXIO1:def 15
.=
((VAL g) . p) => (((VAL g) . q) => ((VAL g) . TFALSUM))
by LTLAXIO1:def 15
;
A4:
( (VAL g) . q = 1 or (VAL g) . q = 0 )
by XBOOLEAN:def 3;
(VAL g) . ('not' (p '&&' q)) =
((VAL g) . (p '&&' q)) => ((VAL g) . TFALSUM)
by LTLAXIO1:def 15
.=
(((VAL g) . p) '&' ((VAL g) . q)) => ((VAL g) . TFALSUM)
by LTLAXIO1:31
;
hence (VAL g) . (('not' (p '&&' q)) => (p => ('not' q))) =
((((VAL g) . p) '&' ((VAL g) . q)) => ((VAL g) . TFALSUM)) => (((VAL g) . p) => (((VAL g) . q) => ((VAL g) . TFALSUM)))
by LTLAXIO1:def 15, A3
.=
1
by A2, A4, A1
;
verum