Theory: comp_unity

Parents


Type constants


Term constants


Axioms


Definitions


Theorems

COMP_UNLESS_thm1
|- !p q FPr GPr.
     (p UNLESS q) (APPEND FPr GPr) = (p UNLESS q) FPr /\ (p UNLESS q) GPr
COMP_ENSURES_thm1
|- !p q FPr GPr.
     (p ENSURES q) (APPEND FPr GPr) =
     (p ENSURES q) FPr /\ (p UNLESS q) GPr \/
     (p ENSURES q) GPr /\ (p UNLESS q) FPr
COMP_ENSURES_cor0
|- !p q FPr GPr.
     (p ENSURES q) FPr /\ (p UNLESS q) GPr ==> (p ENSURES q) (APPEND FPr GPr)
COMP_ENSURES_cor1
|- !p q FPr GPr.
     (p ENSURES q) GPr /\ (p UNLESS q) FPr ==> (p ENSURES q) (APPEND FPr GPr)
COMP_UNITY_cor0
|- !p0 p FPr GPr.
     p INVARIANT (p0,APPEND FPr GPr) =
     p INVARIANT (p0,FPr) /\ p INVARIANT (p0,GPr)
COMP_UNITY_cor1
|- !p FPr GPr. p STABLE APPEND FPr GPr = p STABLE FPr /\ p STABLE GPr
COMP_UNITY_cor2
|- !p q FPr GPr.
     (p UNLESS q) FPr /\ p STABLE GPr ==> (p UNLESS q) (APPEND FPr GPr)
COMP_UNITY_cor3
|- !p0 p FPr GPr.
     p INVARIANT (p0,FPr) /\ p STABLE GPr ==> p INVARIANT (p0,APPEND FPr GPr)
COMP_UNITY_cor4
|- !p q FPr GPr.
     (p ENSURES q) FPr /\ p STABLE GPr ==> (p ENSURES q) (APPEND FPr GPr)
COMP_UNITY_cor5
|- !p q FPr GPr. (p UNLESS q) (APPEND FPr GPr) ==> (p UNLESS q) GPr
COMP_UNITY_cor6
|- !p q FPr GPr. (p UNLESS q) (APPEND FPr GPr) ==> (p UNLESS q) FPr
COMP_UNITY_cor7
|- !p q st FPr. (p UNLESS q) (CONS st FPr) ==> (p UNLESS q) FPr
COMP_UNITY_cor8
|- !p FPr GPr. (p ENSURES ~* p) FPr ==> (p ENSURES ~* p) (APPEND FPr GPr)
COMP_UNITY_cor9
|- !p q FPr GPr.
     p STABLE FPr /\ (p UNLESS q) GPr ==> (p UNLESS q) (APPEND FPr GPr)
COMP_UNITY_cor10
|- !p q FPr GPr. (p UNLESS q) (APPEND FPr GPr) = (p UNLESS q) (APPEND GPr FPr)
COMP_UNITY_cor11
|- !p q FPr GPr.
     (p ENSURES q) (APPEND FPr GPr) = (p ENSURES q) (APPEND GPr FPr)
COMP_UNITY_cor12
|- !p q Pr1 Pr2.
     (p LEADSTO q) (APPEND Pr1 Pr2) = (p LEADSTO q) (APPEND Pr2 Pr1)
COMP_UNITY_cor13
|- !p FPr GPr. p STABLE APPEND FPr GPr = p STABLE APPEND GPr FPr
COMP_UNITY_cor14
|- !p0 p FPr GPr.
     p INVARIANT (p0,APPEND FPr GPr) = p INVARIANT (p0,APPEND GPr FPr)