- EXIST_TRANSITION_thm1
-
|- !p q r Pr.
(p EXIST_TRANSITION q) Pr /\ (!s. q s ==> r s) ==>
(p EXIST_TRANSITION r) Pr
- EXIST_TRANSITION_thm2
-
|- !p Pr. (p EXIST_TRANSITION False) Pr ==> (!s. ~* p s)
- EXIST_TRANSITION_thm3
-
|- !p st Pr. (False EXIST_TRANSITION p) (CONS st Pr)
- ENSURES_thm0
-
|- !p q. (p ENSURES q) [] = F
- ENSURES_thm1
-
|- !p st Pr. (p ENSURES p) (CONS st Pr)
- ENSURES_thm2
-
|- !p q r Pr. (p ENSURES q) Pr /\ (!s. q s ==> r s) ==> (p ENSURES r) Pr
- ENSURES_thm3
-
|- !p Pr. (p ENSURES False) Pr ==> (!s. ~* p s)
- ENSURES_thm4
-
|- !p q p' q' Pr.
(p UNLESS q) Pr /\ (p' ENSURES q') Pr ==>
(p /\* p' ENSURES (p /\* q' \/* p' /\* q) \/* q /\* q') Pr
- ENSURES_thm5
-
|- !p q r Pr. (p ENSURES q) Pr ==> (p \/* r ENSURES q \/* r) Pr
- ENSURES_cor1
-
|- !p q st Pr. (!s. p s ==> q s) ==> (p ENSURES q) (CONS st Pr)
- ENSURES_cor2
-
|- !p q Pr. (p ENSURES q) Pr ==> (p UNLESS q) Pr
- ENSURES_cor3
-
|- !p q r Pr. (p \/* q ENSURES r) Pr ==> (p ENSURES q \/* r) Pr
- ENSURES_cor4
-
|- !p q r Pr. (p ENSURES q \/* r) Pr ==> (p /\* ~* q ENSURES q \/* r) Pr
- ENSURES_cor5
-
|- !p q r Pr. (p ENSURES q) Pr ==> (p ENSURES q \/* r) Pr
- ENSURES_cor6
-
|- !p st Pr. (False ENSURES p) (CONS st Pr)
- ENSURES_cor7
-
|- !p q r Pr. (p ENSURES q) Pr /\ r STABLE Pr ==> (p /\* r ENSURES q /\* r) Pr