- UNLESS_STMT_thm0
-
|- !p st s. (p UNLESS_STMT p) st s
- UNLESS_STMT_thm1
-
|- !p q r st.
(!s. (p UNLESS_STMT q) st s) /\ (!s. q s ==> r s) ==>
(!s. (p UNLESS_STMT r) st s)
- UNLESS_STMT_thm2
-
|- !p q p' q' st.
(!s. (p UNLESS_STMT q) st s) /\ (!s. (p' UNLESS_STMT q') st s) ==>
(!s. (p \/* p' UNLESS_STMT q \/* q') st s)
- UNLESS_STMT_thm3
-
|- !p q p' q' st.
(!s. (p UNLESS_STMT q) st s) /\ (!s. (p' UNLESS_STMT q') st s) ==>
(!s. (p /\* p' UNLESS_STMT (p /\* q' \/* p' /\* q) \/* q /\* q') st s)
- UNLESS_STMT_thm4
-
|- !p q p' q' st.
(!s. (p UNLESS_STMT q) st s) /\ (!s. (p' UNLESS_STMT q') st s) ==>
(!s.
(p \/* p' UNLESS_STMT (~* p /\* q' \/* ~* p' /\* q) \/* q /\* q') st s)
- UNLESS_STMT_thm5
-
|- !P q st.
(!m s. (P m UNLESS_STMT q) st s) ==>
(!s. ((\s. ?n. P n s) UNLESS_STMT q) st s)
- UNLESS_thm1
-
|- !p Pr. (p UNLESS p) Pr
- UNLESS_thm2
-
|- !p Pr. (p UNLESS ~* p) Pr
- UNLESS_thm3
-
|- !p q r Pr. (p UNLESS q) Pr /\ (!s. q s ==> r s) ==> (p UNLESS r) Pr
- UNLESS_thm4
-
|- !p q p' q' Pr.
(p UNLESS q) Pr /\ (p' UNLESS q') Pr ==>
(p /\* p' UNLESS (p /\* q' \/* p' /\* q) \/* q /\* q') Pr
- UNLESS_thm5
-
|- !p q p' q' Pr.
(p UNLESS q) Pr /\ (p' UNLESS q') Pr ==>
(p \/* p' UNLESS (~* p /\* q' \/* ~* p' /\* q) \/* q /\* q') Pr
- UNLESS_thm6
-
|- !p q p' q' Pr.
(p UNLESS q) Pr /\ (p' UNLESS q') Pr ==> (p /\* p' UNLESS q \/* q') Pr
- UNLESS_thm7
-
|- !p q p' q' Pr.
(p UNLESS q) Pr /\ (p' UNLESS q') Pr ==> (p \/* p' UNLESS q \/* q') Pr
- UNLESS_thm8
-
|- !p q r Pr. (p UNLESS q) Pr /\ (q UNLESS r) Pr ==> (p \/* q UNLESS r) Pr
- UNLESS_cor1
-
|- !p q Pr. (!s. p s ==> q s) ==> (p UNLESS q) Pr
- UNLESS_cor2
-
|- !p q Pr. (!s. ~* p s ==> q s) ==> (p UNLESS q) Pr
- UNLESS_cor3
-
|- !p q r Pr. (p /\* ~* q UNLESS q \/* r) Pr = (p UNLESS q \/* r) Pr
- UNLESS_cor4
-
|- !p q r Pr. (p \/* q UNLESS r) Pr ==> (p UNLESS q \/* r) Pr
- UNLESS_cor5
-
|- !p Pr. (p UNLESS True) Pr
- UNLESS_cor6
-
|- !p Pr. (True UNLESS p) Pr
- UNLESS_cor7
-
|- !p Pr. (False UNLESS p) Pr
- UNLESS_cor8
-
|- !p q p' Pr.
(!s. p s /\ ~(q s)) ==>
(!s. p' s) ==>
(!s. p s \/ q s) ==>
((p /\* ~* q UNLESS q) Pr = (p' /\* ~* q UNLESS q) Pr)
- UNLESS_cor9
-
|- !p q p' q' r r' Pr.
(p \/* p' UNLESS q \/* r) Pr /\ (q \/* q' UNLESS p \/* r') Pr ==>
(p \/* p' \/* q \/* q' UNLESS p /\* q \/* r \/* r') Pr
- UNLESS_cor10
-
|- !p q Pr. p \/* q STABLE Pr ==> (p UNLESS q) Pr
- UNLESS_cor11
-
|- !p Pr. (!s. ~* p s) ==> p STABLE Pr
- UNLESS_cor12
-
|- !p Pr. (!s. ~* p s) ==> ~* p STABLE Pr
- UNLESS_cor13
-
|- !p q Pr.
(p UNLESS q) Pr /\ (q UNLESS p) Pr /\ (!s. ~* (p /\* q) s) ==>
p \/* q STABLE Pr
- UNLESS_cor14
-
|- !p q Pr. (p UNLESS ~* q) Pr /\ q STABLE Pr ==> (p UNLESS p /\* ~* q) Pr
- UNLESS_cor15
-
|- !P Q Pr.
(!i. (P i UNLESS P i /\* Q i) Pr) ==> ($!* P UNLESS $!* P /\* $?* Q) Pr
- UNLESS_cor16
-
|- !P Q Pr.
(!i. (P i UNLESS Q i) Pr) ==> (!i. (/<=\* P i UNLESS \<=/* Q i) Pr)
- UNLESS_cor17
-
|- !P q Pr. (!i. (P i UNLESS q) Pr) ==> (!i. (/<=\* P i UNLESS q) Pr)
- UNLESS_cor18
-
|- !P q Pr. (!m. (P m UNLESS q) Pr) ==> ($?* P UNLESS q) Pr
- UNLESS_cor19
-
|- !Pr. False STABLE Pr
- UNLESS_cor20
-
|- !p q Pr. p STABLE Pr /\ q STABLE Pr ==> p /\* q STABLE Pr
- UNLESS_cor21
-
|- !p q Pr. p STABLE Pr /\ q STABLE Pr ==> p \/* q STABLE Pr
- UNLESS_cor22
-
|- !p q r Pr. (p UNLESS q) Pr /\ r STABLE Pr ==> (p /\* r UNLESS q /\* r) Pr