- Safe_Contains
-
|- !P w. P w ==> Safe P w
- Safe_Idem
-
|- !P. Safe (Safe P) = Safe P
- Safe_Mono
-
|- !P Q. (!w. P w ==> Q w) ==> (!w. Safe P w ==> Safe Q w)
- Live_Contains
-
|- !P w. P w ==> Live P w
- Safe_and_Live
-
|- !P w. Safe P w /\ Live P w = P w
- Safe_Live
-
|- !P w. Safe (Live P) w
- Live_Idem
-
|- !P. Live (Live P) = Live P
- Live_Safe
-
|- !P w. Live (Safe P) w
- Safety_Safe
-
|- !P. Safety (Safe P)
- Liveness_Live
-
|- !P. Liveness (Live P)
- Liveness_AND_Safety
-
|- !P. Liveness P /\ Safety P ==> (!w. P w)
- Strongest_safety
-
|- !P Q. Safety Q /\ (!w. P w ==> Q w) ==> (!w. Safe P w ==> Q w)
- Safety_Liveness_Decompose
-
|- !P. ?Q R. Safety Q /\ Liveness R /\ (!w. P w = Q w /\ R w)
- Exists_not_Safety
-
|- ?P. ~(Safety P)