let p, q be Element of LTLB_WFF ; :: thesis: for X being Subset of LTLB_WFF st p '&&' q in tau X holds

( p in tau X & q in tau X )

let X be Subset of LTLB_WFF; :: thesis: ( p '&&' q in tau X implies ( p in tau X & q in tau X ) )

assume p '&&' q in tau X ; :: thesis: ( p in tau X & q in tau X )

then A1: p => (q => TFALSUM) in tau X by Th19;

then 'not' q in tau X by Th19;

hence ( p in tau X & q in tau X ) by A1, Th19; :: thesis: verum

( p in tau X & q in tau X )

let X be Subset of LTLB_WFF; :: thesis: ( p '&&' q in tau X implies ( p in tau X & q in tau X ) )

assume p '&&' q in tau X ; :: thesis: ( p in tau X & q in tau X )

then A1: p => (q => TFALSUM) in tau X by Th19;

then 'not' q in tau X by Th19;

hence ( p in tau X & q in tau X ) by A1, Th19; :: thesis: verum