statement stringlengths 1 33.2k | proof stringlengths 0 198k | type stringclasses 14
values | symbolic_name stringlengths 1 92 | library stringclasses 345
values | filename stringlengths 17 103 | imports listlengths 0 0 | deps listlengths 0 64 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
!e s v. neval e (s |+ (v,s ' v)) = neval e s | Induct
THEN RW_TAC std_ss [neval_def,FAPPLY_FUPDATE_THM] | prove | NEVAL_FUPDATE_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FAPPLY_FUPDATE_THM",
"neval_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!a s v. aeval a (s |+ (v,s ' v)) = aeval a s | Induct
THEN RW_TAC std_ss
[aeval_def,FAPPLY_FUPDATE_THM,NOT_FDOM_FAPPLY_FEMPTY,NEVAL_FUPDATE_LEMMA] | prove | AEVAL_FUPDATE_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FAPPLY_FUPDATE_THM",
"NEVAL_FUPDATE_LEMMA",
"NOT_FDOM_FAPPLY_FEMPTY",
"aeval_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(ACC_PRED p Skip s1 = p)
/\
(ACC_PRED p (GenAssign v e) s1 =
\s2.
if v IN FDOM s1
then ((s2 ' v = Update v e s1 ' v) /\ p(s2 |+ (v,(s1 ' v))))
else ((s2 ' v = Update v e s1 ' v) /\ p(s2 \\ v)))
/\
(ACC_PRED p (Dispose v) s1 =
\s2. if v IN FDOM s1 then p(s2 |+ (v,(s1 ' v))) else... | Define | ACC_PRED_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"IN",
"Update"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!p v e s. p s ==> ACC_PRED p (GenAssign v e) s (Update v e s) | RW_TAC std_ss []
THEN Cases_on `e`
THEN RW_TAC std_ss
[ACC_PRED_def,UpdateCases,FUPDATE_EQ,FAPPLY_FUPDATE,UpdateCases,
FUPDATE_ID,NEVAL_FUPDATE_LEMMA,AEVAL_FUPDATE_LEMMA,
DOMSUB_FUPDATE,DOMSUB_NOT_IN_DOM] | store_thm | ACC_PRED_ASSIGN_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_PRED_def",
"AEVAL_FUPDATE_LEMMA",
"DOMSUB_FUPDATE",
"DOMSUB_NOT_IN_DOM",
"FAPPLY_FUPDATE",
"FUPDATE_EQ",
"FUPDATE_ID",
"NEVAL_FUPDATE_LEMMA",
"Update",
"UpdateCases"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!p v s. p s ==> ACC_PRED p (Dispose v) s (s \\ v) | RW_TAC std_ss
[ACC_PRED_def,FUPDATE_EQ,FAPPLY_FUPDATE,
FUPDATE_ID,NEVAL_FUPDATE_LEMMA,AEVAL_FUPDATE_LEMMA,
DOMSUB_FUPDATE,DOMSUB_NOT_IN_DOM,FUPDATE_DOMSUB] | store_thm | ACC_PRED_DISPOSE_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_PRED_def",
"AEVAL_FUPDATE_LEMMA",
"DOMSUB_FUPDATE",
"DOMSUB_NOT_IN_DOM",
"FAPPLY_FUPDATE",
"FUPDATE_DOMSUB",
"FUPDATE_EQ",
"FUPDATE_ID",
"NEVAL_FUPDATE_LEMMA"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!con1 con2.
SMALL_EVAL con1 con2
==>
(\con1 con2.
p(SND con1)
==>
ACC_PRED p (HD(FST con1)) (SND con1) (SND con2))
con1 con2 | IndDefRules.RULE_TAC
(IndDefRules.derive_mono_strong_induction [] (small_rules,small_induction))
THEN RW_TAC list_ss [ACC_PRED_ASSIGN_LEMMA,ACC_PRED_DISPOSE_LEMMA]
THEN RW_TAC list_ss [ACC_PRED_def] | store_thm | SMALL_EVAL_ACC_PRED_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_PRED_ASSIGN_LEMMA",
"ACC_PRED_DISPOSE_LEMMA",
"ACC_PRED_def",
"FST",
"HD",
"SND"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c p l1 l2 s1 s2.
p s1
==>
SMALL_EVAL (c::l1,s1) (l2,s2)
==>
ACC_PRED p c s1 s2 | METIS_TAC
[SMALL_EVAL_ACC_PRED_LEMMA,listTheory.HD,pairTheory.FST,pairTheory.SND] | store_thm | SMALL_EVAL_ACC_PRED | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST",
"HD",
"SMALL_EVAL_ACC_PRED_LEMMA",
"SND"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c p l1 l2 s1 s2.
p s1
==>
(STEP1(c::l1,s1) = (l2, RESULT s2))
==>
ACC_PRED p c s1 s2 | METIS_TAC[SMALL_EVAL_ACC_PRED,STEP1_SMALL_EVAL] | store_thm | STEP1_ACC_PRED | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SMALL_EVAL_ACC_PRED",
"STEP1",
"STEP1_SMALL_EVAL"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
ACC_SMALL_EVAL (con1, p1) (con2, p2) =
SMALL_EVAL con1 con2 /\ (p2 = ACC_PRED p1 (HD(FST con1)) (SND con1)) | Define | ACC_SMALL_EVAL_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_SMALL_EVAL",
"FST",
"HD",
"SND",
"p1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(ACC_SMALL_EVAL (([], s1), p1) ((l2, s2), p2) = F)
/\
(ACC_SMALL_EVAL ((c :: l1, s1), p1) ((l2, s2), p2) =
SMALL_EVAL (c :: l1, s1) (l2, s2) /\ (p2 = ACC_PRED p1 c s1)) | RW_TAC list_ss [ACC_SMALL_EVAL_def,SMALL_EVAL_NIL] | store_thm | ACC_SMALL_EVAL | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_SMALL_EVAL_def",
"SMALL_EVAL_NIL",
"p1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!x. IS_SOME x = ?y. x = SOME y | Cases
THEN RW_TAC std_ss [] | store_thm | IS_SOME_EXISTS | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(!s1 p1 l2 s2 p2.
ACC_SMALL_EVAL (([], s1), p1) ((l2, s2), p2) = F)
/\
(!s1 l p.
ACC_SMALL_EVAL ((Skip :: l, s1), p) ((l, s1), p))
/\
(!s1 v e l p.
v IN FDOM s1
==>
ACC_SMALL_EVAL
((GenAssign v e :: l, s1), p)
((l,
Update v e s1),
... | RW_TAC list_ss
([ACC_SMALL_EVAL,ACC_PRED_def,FUN_EQ_THM,IS_SOME_EXISTS]
@ small_rulel)
THEN RW_TAC std_ss []
THEN METIS_TAC [] | store_thm | ACC_SMALL_EVAL_CLAUSES | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_PRED_def",
"ACC_SMALL_EVAL",
"FUN_EQ_THM",
"IN",
"IS_SOME_EXISTS",
"Update",
"p1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2 s1 s2 p1 p2.
ACC_SMALL_EVAL ((l1,s1),p1) ((l2,s2),p2) /\ p1 s1 ==> p2 s2 | Cases
THEN RW_TAC list_ss [ACC_SMALL_EVAL]
THEN METIS_TAC[SMALL_EVAL_ACC_PRED] | store_thm | ACC_SMALL_EVAL_TRUE | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_SMALL_EVAL",
"SMALL_EVAL_ACC_PRED",
"p1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!con1 con2 p1 p2.
ACC_SMALL_EVAL (con1,p1) (con2,p2) ==> SMALL_EVAL con1 con2 | METIS_TAC[ACC_SMALL_EVAL_def] | store_thm | ACC_SMALL_EVAL_SMALL_EVAL | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_SMALL_EVAL",
"ACC_SMALL_EVAL_def",
"p1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2 s1 s2 p1 p2.
p1 s1
==>
ACC_SMALL_EVAL ((l1,s1),p1) ((l2,s2),p2)
==>
SMALL_EVAL (l1,s1) (l2,s2) /\ p2 s2 | METIS_TAC[ACC_SMALL_EVAL_TRUE,ACC_SMALL_EVAL_SMALL_EVAL] | store_thm | ACC_SMALL_EVAL_THM | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_SMALL_EVAL",
"ACC_SMALL_EVAL_SMALL_EVAL",
"ACC_SMALL_EVAL_TRUE",
"p1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
ACC_STEP_BIND m f = case m of
((l, TIMEOUT s), p) -> ((l, TIMEOUT s), p)
|| ((l, ERROR s), p) -> ((l, ERROR s), p)
|| ((l, RESULT s), p) -> f((l, s), p) | Define | ACC_STEP_BIND_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
ACC_STEP_RETURN x = ((FST(FST x), RESULT(SND(FST x))), SND x) | Define | ACC_STEP_RETURN_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST",
"SND"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
((ACC_STEP_RETURN x) >>= f = f x)
/\
(m >>= ACC_STEP_RETURN = m)
/\
((m >>= f) >>= g = m >>= (\x. (f x) >>= g)) | RW_TAC std_ss [ACC_STEP_BIND_def, ACC_STEP_RETURN_def]
THEN Cases_on `m`
THEN Cases_on `q`
THEN Cases_on `r'`
THEN RW_TAC (srw_ss()) [] | store_thm | ACC_STEP_MONAD_LAWS | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_STEP_BIND_def",
"ACC_STEP_RETURN_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l s p. ((l, RESULT s), p) >>= f = f((l,s),p) | RW_TAC std_ss [ACC_STEP_BIND_def, ACC_STEP_RETURN_def] | store_thm | ACC_STEP_BIND_RESULT | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_STEP_BIND_def",
"ACC_STEP_RETURN_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
ACC_STEP1 (con, p) =
(STEP1 con,
if NULL(FST con) then p else ACC_PRED p (HD(FST con)) (SND con)) | Define | ACC_STEP1_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST",
"HD",
"NULL",
"SND",
"STEP1"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(ACC_STEP n (([],s),p) = (([], RESULT s), p))
/\
(ACC_STEP 0 ((l,s),p) = ((l, TIMEOUT s), p))
/\
(ACC_STEP (SUC n) ((l,s),p) = ACC_STEP1 ((l,s),p) >>= ACC_STEP n) | Define | ACC_STEP_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_STEP"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!l. ~(l = []) = ?x l'. l = x :: l' | Induct
THEN RW_TAC list_ss [] | prove | NOT_EMPTY_EXISTS | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!n l s p.
ACC_STEP n ((l,s),p) =
if (l = [])
then (([], RESULT s), p) else
if (n = 0)
then ((l, TIMEOUT s), p)
else ACC_STEP1 ((l,s),p) >>= ACC_STEP (n-1) | Cases
THEN RW_TAC std_ss [ACC_STEP_def]
THEN FULL_SIMP_TAC std_ss [NOT_EMPTY_EXISTS]
THEN RW_TAC std_ss [ACC_STEP_def,ACC_STEP_BIND_def] | store_thm | ACC_STEP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_STEP_BIND_def",
"ACC_STEP_def",
"NOT_EMPTY_EXISTS"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!n l s1 s2 P Q.
P s1 /\ (ACC_STEP n ((l,s1),P) = (([], RESULT s2), Q))
==>
(STEP n (l,s1) = ([], RESULT s2)) /\ Q s2 | Induct
THEN RW_TAC std_ss [ACC_STEP_def,STEP]
THEN RW_TAC std_ss []
THEN FULL_SIMP_TAC (srw_ss()) [ACC_STEP_def,NOT_EMPTY_EXISTS]
THEN RW_TAC std_ss [STEP_SUC]
THEN FULL_SIMP_TAC (srw_ss()) [ACC_STEP_def,NOT_EMPTY_EXISTS]
THEN RW_TAC std_ss []
THEN FULL_SIMP_TAC (srw_ss())
[ACC_STE... | store_thm | ACC_STEP_STEP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_STEP",
"ACC_STEP1_def",
"ACC_STEP_BIND_def",
"ACC_STEP_def",
"NOT_EMPTY_EXISTS",
"STEP",
"STEP1",
"STEP1_ACC_PRED",
"STEP_BIND_def",
"STEP_SUC"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!P c R.
(!s1. ?n s2. ACC_STEP n (([c],s1),P) = (([], RESULT s2), R s1))
==>
!s1 s2. P s1 /\ EVAL c s1 s2 ==> R s1 s2 | RW_TAC std_ss [EVAL_STEP]
THEN `?n s2. ACC_STEP n (([c],s1),P) = (([],RESULT s2),R s1)` by METIS_TAC[]
THEN IMP_RES_TAC ACC_STEP_STEP
THEN `n <= n' \/ n' <= n` by DECIDE_TAC
THEN IMP_RES_TAC STEP_MONO
THEN `RESULT s2 = RESULT s2'` by METIS_TAC[pairTheory.PAIR_EQ]
THEN FULL_SIMP_TAC (srw_ss()) [] | store_thm | SPEC_ACC_STEP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ACC_STEP",
"ACC_STEP_STEP",
"EVAL_STEP",
"PAIR_EQ",
"STEP_MONO"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!A P c Q f.
(!s. A s ==> P s ==> (EVAL c s (f s) /\ (Q(f s) = T)))
==>
SPEC (\s. P s /\ A s) c Q | RW_TAC std_ss [SPEC_def]
THEN RES_TAC
THEN IMP_RES_TAC EVAL_DETERMINISTIC
THEN RW_TAC std_ss [] | store_thm | EVAL_SPEC_THM | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_DETERMINISTIC",
"SPEC_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!f p. f |+ p = f \\ (FST p) |+ p | RW_TAC std_ss []
THEN Cases_on `p`
THEN RW_TAC std_ss []
THEN METIS_TAC [FUPDATE_PRUNE_LEMMA] | store_thm | FUPDATE_PRUNE | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!f p. f |+ p = f |++ [p] | RW_TAC list_ss [FUPDATE_LIST_THM] | store_thm | FUPDATE_LIST_FOLD_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FUPDATE_LIST_THM"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!pre prog post. RSPEC pre prog post = IMP pre post prog | METIS_TAC[IMP_def] | store_thm | IMP_INTRO_THM | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"IMP_def",
"pre"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
ILOG(tm:bool) = tm | Define | ILOG_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(STRAIGHT Skip = T)
/\
(STRAIGHT (GenAssign v e) = T)
/\
(STRAIGHT (Dispose v) = F)
/\
(STRAIGHT (Seq c1 c2) = STRAIGHT c1 /\ STRAIGHT c2)
/\
(STRAIGHT (Cond b c1 c2) = STRAIGHT c1 /\ STRAIGHT c2)
/\
(STRAIGHT (AnWhile b R c) = F)
/\
(STRAIGHT (Local v c) = F) | Define | STRAIGHT_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(UPDATE_LIST [] (v,x) = [(v,x)])
/\
(UPDATE_LIST ((v2,x2) :: l) (v1,x1) =
if v1 = v2 then (v1,x1) :: l else (v2,x2) :: UPDATE_LIST l (v1,x1)) | Define | UPDATE_LIST_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(ZIP_LIST (b:bool) l1 [] = [])
/\
(ZIP_LIST (b:bool) [] l2 = [])
/\
(ZIP_LIST b ((v1,x1) :: l1) ((v2,x2) :: l2) =
(v1, (if b then x1 else x2)) :: ZIP_LIST b l1 l2) | Define | ZIP_LIST_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(STRAIGHT_RUN Skip l = l)
/\
(STRAIGHT_RUN (GenAssign v e) l =
UPDATE_LIST l (v, naeval e (FEMPTY |++ l)))
/\
(STRAIGHT_RUN (Seq c1 c2) s = STRAIGHT_RUN c2 (STRAIGHT_RUN c1 s))
/\
(STRAIGHT_RUN (Cond b c1 c2) l =
ZIP_LIST (beval b (FEMPTY |++ l)) (STRAIGHT_RUN c1 l) (STRAIGHT_RUN c2 l)) | Define | STRAIGHT_RUN_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
DISTINCT_VARS l = ALL_DISTINCT(MAP FST l) | Define | DISTINCT_VARS_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"FST",
"MAP"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!l. ~(MEM v (MAP FST l)) /\ DISTINCT_VARS l
==> !fm x y. fm |+ (v,x) |++ l = (fm |+ (v,y) |++ l) |+ (v,x) | Induct
THEN RW_TAC std_ss [FUPDATE_LIST_THM,FUPDATE_EQ]
THEN Cases_on `h`
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT]
THEN METIS_TAC[FUPDATE_EQ,FUPDATE_COMMUTES] | store_thm | FUPDATE_LIST_FUPDATE_NOT_MEM | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FST",
"FUPDATE_COMMUTES",
"FUPDATE_EQ",
"FUPDATE_LIST_THM",
"MAP",
"MEM"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l. DISTINCT_VARS l
==> !fm v x. fm |++ UPDATE_LIST l (v,x) = (fm |++ l) |+ (v,x) | Induct
THEN RW_TAC std_ss [UPDATE_LIST_def,FUPDATE_LIST_THM]
THEN Cases_on `h`
THEN FULL_SIMP_TAC std_ss [UPDATE_LIST_def,FUPDATE_LIST_THM,listTheory.ALL_DISTINCT]
THEN Cases_on `v = q`
THEN FULL_SIMP_TAC list_ss
[UPDATE_LIST_def,FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT]
... | store_thm | UPDATE_LIST_FUPDATE | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FUPDATE_LIST_FUPDATE_NOT_MEM",
"FUPDATE_LIST_THM",
"UPDATE_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l. MAP FST (UPDATE_LIST l (v,x)) =
if MEM v (MAP FST l) then MAP FST l else (MAP FST l) ++ [v] | Induct
THEN RW_TAC list_ss [DISTINCT_VARS_def,listTheory.ALL_DISTINCT,UPDATE_LIST_def]
THEN Cases_on `h`
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT,UPDATE_LIST_def]
THEN Cases_on `q = v`
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DIST... | prove | MAP_FST_UPDATE_LIST | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FST",
"FUPDATE_LIST_THM",
"MAP",
"MEM",
"UPDATE_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l. DISTINCT_VARS l ==> !v x. DISTINCT_VARS(UPDATE_LIST l (v,x)) | Induct
THEN RW_TAC list_ss [DISTINCT_VARS_def,listTheory.ALL_DISTINCT,UPDATE_LIST_def]
THEN Cases_on `h`
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT,UPDATE_LIST_def]
THEN Cases_on `q = v`
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DIST... | store_thm | UpdateDISTINCT | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FST",
"FUPDATE_LIST_THM",
"MAP",
"MAP_FST_UPDATE_LIST",
"MEM",
"UPDATE_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2 b x. MEM x (MAP FST (ZIP_LIST b l1 l2)) ==> MEM x (MAP FST l1) | Induct
THENL[ALL_TAC,GEN_TAC]
THEN Induct
THEN RW_TAC list_ss [DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def]
THEN Cases_on `h`
THEN TRY(Cases_on `h'`)
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def]
THEN METIS_TAC[] | prove | MAP_FST_SUBSET_ZIP_LIST | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FST",
"FUPDATE_LIST_THM",
"MAP",
"MEM",
"ZIP_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2. DISTINCT_VARS l1 /\ DISTINCT_VARS l2
==> !b. DISTINCT_VARS(ZIP_LIST b l1 l2) | Induct
THENL[ALL_TAC,GEN_TAC]
THEN Induct
THEN RW_TAC list_ss [DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def]
THEN Cases_on `h`
THEN TRY(Cases_on `h'`)
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def]
THEN METIS_TAC[MAP_F... | store_thm | ZIP_LIST_DISTINCT | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FUPDATE_LIST_THM",
"MAP_FST_SUBSET_ZIP_LIST",
"ZIP_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c. STRAIGHT c ==> !l. DISTINCT_VARS l ==> DISTINCT_VARS(STRAIGHT_RUN c l) | Induct
THEN RW_TAC std_ss [rules,STRAIGHT_RUN_def,STRAIGHT_def]
THEN TRY(Cases_on `s0`)
THEN RW_TAC std_ss
[SEQ_THM,IF_THM,rules,GEN_ASSIGN_THM,UpdateCases,
STRAIGHT_RUN_def,UPDATE_LIST_FUPDATE,UpdateDISTINCT,ZIP_LIST_DISTINCT] | store_thm | STRAIGHT_RUN_DISTINCT | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"GEN_ASSIGN_THM",
"IF_THM",
"SEQ_THM",
"STRAIGHT_RUN_def",
"STRAIGHT_def",
"UPDATE_LIST_FUPDATE",
"UpdateCases",
"UpdateDISTINCT",
"ZIP_LIST_DISTINCT"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2. (LENGTH l1 = LENGTH l2) ==> (ZIP_LIST T l1 l2 = l1) | Induct
THENL[ALL_TAC,GEN_TAC]
THEN Induct
THEN RW_TAC list_ss [DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def]
THEN Cases_on `h`
THEN TRY(Cases_on `h'`)
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def] | store_thm | ZIP_LIST_T | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FUPDATE_LIST_THM",
"LENGTH",
"ZIP_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2. (MAP FST l1 = MAP FST l2) ==> (ZIP_LIST F l1 l2 = l2) | Induct
THENL[ALL_TAC,GEN_TAC]
THEN Induct
THEN RW_TAC list_ss [DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def]
THEN Cases_on `h`
THEN TRY(Cases_on `h'`)
THEN FULL_SIMP_TAC list_ss
[FUPDATE_LIST_THM,DISTINCT_VARS_def,listTheory.ALL_DISTINCT,ZIP_LIST_def] | store_thm | ZIP_LIST_F | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ALL_DISTINCT",
"DISTINCT_VARS_def",
"FST",
"FUPDATE_LIST_THM",
"MAP",
"ZIP_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(VARS Skip = {})
/\
(VARS (GenAssign v e) = {v})
/\
(VARS (Seq c1 c2) = VARS c1 UNION VARS c2)
/\
(VARS (Cond b c1 c2) = VARS c1 UNION VARS c2)
/\
(VARS (AnWhile b R c) = VARS c)
/\
(VARS (Local v c) = v INSERT VARS c) | Define | VARS_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"UNION"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(LIST_UNION [] l2 = l2)
/\
(LIST_UNION (x::l1) l2 = if MEM x l2 then LIST_UNION l1 l2 else x :: LIST_UNION l1 l2) | Define | LIST_UNION_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"MEM"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!l1 l2. set(LIST_UNION l1 l2) = set l1 UNION set l2 | Induct
THEN RW_TAC std_ss
[LIST_UNION_def,listTheory.LIST_TO_SET_THM,UNION_EMPTY,
INSERT_UNION,GSYM listTheory.IN_LIST_TO_SET] | store_thm | LIST_UNION_UNION | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"INSERT_UNION",
"LIST_TO_SET_THM",
"LIST_UNION_def",
"UNION",
"UNION_EMPTY"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(VARL Skip = [])
/\
(VARL (GenAssign v e) = [v])
/\
(VARL (Seq c1 c2) = LIST_UNION (VARL c1) (VARL c2))
/\
(VARL (Cond b c1 c2) = LIST_UNION (VARL c1) (VARL c2))
/\
(VARL (AnWhile b R c) = VARL c)
/\
(VARL (Local v c) = LIST_UNION [v] (VARL c)) | Define | VARL_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(SIMPLE Skip = T)
/\
(SIMPLE (GenAssign v e) = T)
/\
(SIMPLE (Dispose v) = F)
/\
(SIMPLE (Seq c1 c2) = SIMPLE c1 /\ SIMPLE c2)
/\
(SIMPLE (Cond b c1 c2) = SIMPLE c1 /\ SIMPLE c2)
/\
(SIMPLE (AnWhile b R c) = SIMPLE c)
/\
(SIMPLE (Local v c) = SIMPLE c) | Define | SIMPLE_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!c. SIMPLE c ==> (VARS c = set(VARL c)) | Induct
THEN RW_TAC std_ss
[SIMPLE_def,VARS_def,VARL_def,listTheory.LIST_TO_SET_THM,
LIST_UNION_UNION,listTheory.SET_TO_LIST_INV]
THEN METIS_TAC [INSERT_SING_UNION] | store_thm | VARS_VARL | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"INSERT_SING_UNION",
"LIST_TO_SET_THM",
"LIST_UNION_UNION",
"SET_TO_LIST_INV",
"SIMPLE_def",
"VARL_def",
"VARS_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!l1 l2 l b. (MAP FST l1 = l) /\ (MAP FST l2 = l) ==> (MAP FST (ZIP_LIST b l1 l2) = l) | Induct
THENL[ALL_TAC,GEN_TAC]
THEN Induct
THEN RW_TAC list_ss [ZIP_LIST_def]
THEN Cases_on `h`
THEN Cases_on `h'`
THEN FULL_SIMP_TAC list_ss [ZIP_LIST_def] | prove | MAP_FST_ZIP_LIST | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST",
"MAP",
"ZIP_LIST_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
VARS_IN c l = !v. v IN (VARS c) ==> MEM v (MAP FST l) | Define | VARS_IN_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST",
"IN",
"MAP",
"MEM"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!c l. STRAIGHT c /\ VARS_IN c l
==> (MAP FST (STRAIGHT_RUN c l) = MAP FST l) | Induct
THEN TRY(Cases_on `s0`)
THEN RW_TAC list_ss
[STRAIGHT_def,VARS_def,NOT_IN_EMPTY,IN_SING,STRAIGHT_RUN_def,
MAP_FST_UPDATE_LIST,IN_UNION,VARS_IN_def,MAP_FST_ZIP_LIST,VARS_IN_def] | prove | VARS_STRAIGHT_RUN | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FST",
"IN_SING",
"IN_UNION",
"MAP",
"MAP_FST_UPDATE_LIST",
"MAP_FST_ZIP_LIST",
"NOT_IN_EMPTY",
"STRAIGHT_RUN_def",
"STRAIGHT_def",
"VARS_IN_def",
"VARS_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c l. STRAIGHT c /\ VARS_IN c l
==> (LENGTH(STRAIGHT_RUN c l) = LENGTH l) | METIS_TAC[VARS_IN_def,rich_listTheory.LENGTH_MAP,VARS_STRAIGHT_RUN] | prove | VARS_STRAIGHT_RUN_COR | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"LENGTH",
"LENGTH_MAP",
"VARS_IN_def",
"VARS_STRAIGHT_RUN"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c l. STRAIGHT c
==> VARS_IN c l
==> DISTINCT_VARS l
==> (EVAL c (FEMPTY |++ l) (FEMPTY |++ STRAIGHT_RUN c l)) | Induct
THEN RW_TAC std_ss
[VARS_IN_def,STRAIGHT_def, rules, STRAIGHT_RUN_def,VARS_def,IN_UNION]
THEN TRY(Cases_on `s0`)
THEN RW_TAC std_ss
[SEQ_THM,IF_THM,rules,GEN_ASSIGN_THM,Update_def,
STRAIGHT_RUN_def,UPDATE_LIST_FUPDATE]
THEN METIS_TAC
[ZIP_LIST_DISTINCT,STR... | store_thm | STRAIGHT_RUN_EVAL | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"GEN_ASSIGN_THM",
"IF_THM",
"IN_UNION",
"SEQ_THM",
"STRAIGHT_RUN_DISTINCT",
"STRAIGHT_RUN_def",
"STRAIGHT_def",
"UPDATE_LIST_FUPDATE",
"Update_def",
"VARS_IN_def",
"VARS_STRAIGHT_RUN",
"VARS_STRAIGHT_RUN_COR",
"VARS_def",
"ZIP_LIST_DISTINCT",
"ZIP_LIST_F",
"ZIP_LIST_T"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
STRAIGHT_RUN_CONT c (cont:(string#value)list->'a) l = cont(STRAIGHT_RUN c l) | Define | STRAIGHT_RUN_CONT_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"STRAIGHT_RUN_CONT",
"value"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(!cont l.
STRAIGHT_RUN_CONT Skip cont l = cont l)
/\
(!cont l v e_or_a.
STRAIGHT_RUN_CONT (GenAssign v e_or_a) cont l =
cont(UPDATE_LIST l (v, naeval e_or_a (FEMPTY |++ l))))
/\
(!cont l v e.
STRAIGHT_RUN_CONT (Assign v e) cont l =
cont(UPDATE_LIST l (v, Sca... | RW_TAC std_ss
[STRAIGHT_RUN_CONT_def,STRAIGHT_RUN_def,Assign_def,
ArrayAssign_def,naeval_def]
THEN METIS_TAC
[VARS_STRAIGHT_RUN_COR,ZIP_LIST_T,VARS_STRAIGHT_RUN,ZIP_LIST_F] | store_thm | STRAIGHT_RUN_CONT | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ArrayAssign_def",
"Assign_def",
"STRAIGHT_RUN_CONT_def",
"STRAIGHT_RUN_def",
"VARS_STRAIGHT_RUN",
"VARS_STRAIGHT_RUN_COR",
"ZIP_LIST_F",
"ZIP_LIST_T",
"naeval_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SOME_BIND m f = case m of
SOME s -> f s
|| NONE -> NONE | Define | SOME_BIND_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
((SOME x) >>= f = f x)
/\
(m >>= SOME = m)
/\
((m >>= f) >>= g = m >>= (\x. (f x) >>= g)) | RW_TAC std_ss [SOME_BIND_def]
THEN Cases_on `m`
THEN RW_TAC (srw_ss()) [] | store_thm | SOME_MONAD_LAWS | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_BIND_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(SOME_FUNPOW g 0 x = SOME x)
/\
(SOME_FUNPOW g (SUC n) x =
case g x of
SOME y -> SOME_FUNPOW g n y
|| NONE -> NONE) | Define | SOME_FUNPOW_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(SOME_FUNPOW g 0 x = SOME x)
/\
(SOME_FUNPOW g (SUC n) x = (g x >>= SOME_FUNPOW g n)) | METIS_TAC[SOME_BIND_def,SOME_FUNPOW_def] | store_thm | SOME_FUNPOW | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_BIND_def",
"SOME_FUNPOW_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!P. (?n. P n) ==> ((LEAST n. P n) = @n. P n /\ !m. m < n ==> ~(P m)) | RW_TAC std_ss []
THEN SELECT_ELIM_TAC
THEN RW_TAC std_ss []
THEN METIS_TAC [LESS_LESS_CASES,LEAST_INTRO,LEAST_EXISTS,LEAST_EXISTS_IMP] | store_thm | EXISTS_LEAST | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"LEAST_EXISTS",
"LEAST_EXISTS_IMP",
"LEAST_INTRO",
"LESS_LESS_CASES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SOME_ITER P g x =
if (?n. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x)))
then SOME_FUNPOW
g
(@n. (IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x)))
/\
!m. m < n ==> ~(IS_SOME(SOME_FUNPOW g m x) /\ P(THE(SOME_FUNPOW g m x))))
x
... | Define | SOME_ITER_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_ITER"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
SOME_ITER P g x =
if (?n. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x)))
then
SOME_FUNPOW g (LEAST n. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x))) x
else NONE | METIS_TAC
[BETA_RULE
(ISPEC
``\n:num. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x))``
EXISTS_LEAST),
SOME_ITER_def] | store_thm | SOME_ITER | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EXISTS_LEAST",
"SOME_FUNPOW",
"SOME_ITER_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SOME_ITER P g x =
if P x then SOME x else g x >>= SOME_ITER P g | REWRITE_TAC [SOME_ITER_def,SOME_BIND_def]
THEN COND_CASES_TAC
THENL
[POP_ASSUM STRIP_ASSUME_TAC
THEN COND_CASES_TAC
THENL
[SELECT_ELIM_TAC
THEN CONJ_TAC
THENL
[Q.EXISTS_TAC `0`
THEN ASM_REWRITE_TAC [SOME_FUNPOW_def, NOT_LESS_0]
... | store_thm | SOME_ITER_REC | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"LESS_0",
"LESS_LESS_CASES",
"LESS_MONO_EQ",
"NOT_LESS_0",
"SOME_BIND_def",
"SOME_FUNPOW",
"SOME_FUNPOW_def",
"SOME_ITER",
"SOME_ITER_def",
"WOP",
"num_CASES",
"option_CLAUSES",
"th"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(SOME_ITER P g x = NONE) =
~ ?n. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x)) | RW_TAC std_ss [SOME_ITER_def]
THENL
[SELECT_ELIM_TAC
THEN RW_TAC (srw_ss()) []
THENL
[Q.EXISTS_TAC `LEAST n. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x))`
THEN RW_TAC (srw_ss()) []
THEN METIS_TAC
[BETA_RULE
(ISPEC
... | store_thm | SOME_ITER_NONE | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"LEAST_EXISTS_IMP",
"SOME_FUNPOW",
"SOME_ITER",
"SOME_ITER_def",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(?y. SOME_ITER P g x = SOME y)
==>
?n. IS_SOME(SOME_FUNPOW g n x)
/\
P(THE(SOME_FUNPOW g n x))
/\
(SOME_ITER P g x = SOME_FUNPOW g n x) | RW_TAC std_ss []
THEN Cases_on `?n. IS_SOME (SOME_FUNPOW g n x) /\ P (THE (SOME_FUNPOW g n x))`
THEN FULL_SIMP_TAC (srw_ss()) [SOME_ITER]
THEN RW_TAC (srw_ss()) []
THEN METIS_TAC
[BETA_RULE
(ISPEC
``\n:num. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x))``
... | prove | SOME_ITER_SOME1 | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"LEAST_EXISTS_IMP",
"SOME_FUNPOW",
"SOME_ITER",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(?n. IS_SOME(SOME_FUNPOW g n x)
/\
P(THE(SOME_FUNPOW g n x))
/\
(SOME_ITER P g x = SOME_FUNPOW g n x))
==>
?y. SOME_ITER P g x = SOME y | RW_TAC std_ss []
THEN Induct_on `n`
THEN RW_TAC (srw_ss()) [SOME_FUNPOW_def]
THEN Cases_on `g x`
THEN FULL_SIMP_TAC (srw_ss()) []
THEN METIS_TAC[option_CLAUSES] | prove | SOME_ITER_SOME2 | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_FUNPOW_def",
"SOME_ITER",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(?y. SOME_ITER P g x = SOME y) =
?n. IS_SOME(SOME_FUNPOW g n x)
/\
P(THE(SOME_FUNPOW g n x))
/\
(SOME_ITER P g x = SOME_FUNPOW g n x) | METIS_TAC[SOME_ITER_SOME1,SOME_ITER_SOME2] | store_thm | SOME_ITER_SOME | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_ITER",
"SOME_ITER_SOME1",
"SOME_ITER_SOME2"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(?y. SOME_ITER P g x = SOME y) =
(?n. IS_SOME (SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x)))
/\
(SOME_ITER P g x =
SOME_FUNPOW
g
(LEAST n. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOME_FUNPOW g n x)))
x) | RW_TAC std_ss [SOME_ITER]
THEN Q.EXISTS_TAC
`THE(SOME_FUNPOW g
(LEAST n.
IS_SOME (SOME_FUNPOW g n x) /\ P (THE (SOME_FUNPOW g n x)))
x)`
THEN METIS_TAC
[BETA_RULE
(ISPEC
``\n:num. IS_SOME(SOME_FUNPOW g n x) /\ P(THE(SOM... | store_thm | SOME_ITER_LEAST | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"LEAST_EXISTS_IMP",
"SOME_FUNPOW",
"SOME_ITER",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SOME_WHILE P = SOME_ITER ($~ o P) | Define | SOME_WHILE_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_ITER",
"SOME_WHILE"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
SOME_WHILE P g x =
if (?n. IS_SOME(SOME_FUNPOW g n x) /\ ~P(THE(SOME_FUNPOW g n x)))
then
SOME_FUNPOW g (LEAST n. IS_SOME(SOME_FUNPOW g n x) /\ ~P(THE(SOME_FUNPOW g n x))) x
else NONE | RW_TAC std_ss [SOME_WHILE_def,SOME_ITER] | store_thm | SOME_WHILE | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_ITER",
"SOME_WHILE_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SOME_WHILE P g x =
if P x then g x >>= SOME_WHILE P g else SOME x | RW_TAC std_ss [SOME_WHILE_def,SOME_ITER_REC]
THEN METIS_TAC[] | store_thm | SOME_WHILE_REC | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_ITER_REC",
"SOME_WHILE",
"SOME_WHILE_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(SOME_WHILE P g x = NONE) =
~?n. IS_SOME(SOME_FUNPOW g n x) /\ ~P(THE(SOME_FUNPOW g n x)) | RW_TAC std_ss [SOME_WHILE_def,SOME_ITER_NONE] | store_thm | SOME_WHILE_NONE | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_ITER_NONE",
"SOME_WHILE",
"SOME_WHILE_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(SOME_WHILE P g x = NONE) =
P x /\ ((g x = NONE) \/ ?z. (g x = SOME z) /\ (SOME_WHILE P g z = NONE)) | RW_TAC (srw_ss()) [Once SOME_WHILE_REC,SOME_BIND_def]
THEN Cases_on `g x`
THEN FULL_SIMP_TAC (srw_ss()) [] | store_thm | SOME_WHILE_NONE_CASES | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_BIND_def",
"SOME_WHILE",
"SOME_WHILE_REC"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(?y. SOME_WHILE P g x = SOME y) =
?n. IS_SOME(SOME_FUNPOW g n x)
/\
~P(THE(SOME_FUNPOW g n x))
/\
(SOME_WHILE P g x = SOME_FUNPOW g n x) | RW_TAC std_ss [SOME_WHILE_def,SOME_ITER_SOME] | store_thm | SOME_WHILE_SOME | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_ITER_SOME",
"SOME_WHILE",
"SOME_WHILE_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(SOME_WHILE P g x = SOME y) =
if P x
then (?z. (g x = SOME z) /\ (SOME_WHILE P g z = SOME y))
else (x = y) | RW_TAC (srw_ss()) [Once SOME_WHILE_REC,SOME_BIND_def]
THEN Cases_on `g x`
THEN FULL_SIMP_TAC (srw_ss()) [] | store_thm | SOME_WHILE_SOME_CASES | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_BIND_def",
"SOME_WHILE",
"SOME_WHILE_REC"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(?y. SOME_WHILE P g x = SOME y) =
(?n. IS_SOME (SOME_FUNPOW g n x) /\ ~P(THE(SOME_FUNPOW g n x)))
/\
(SOME_WHILE P g x =
SOME_FUNPOW
g
(LEAST n. IS_SOME(SOME_FUNPOW g n x) /\ ~P(THE(SOME_FUNPOW g n x)))
x) | RW_TAC std_ss [SOME_WHILE_def,SOME_ITER_LEAST] | store_thm | SOME_WHILE_LEAST | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_FUNPOW",
"SOME_ITER_LEAST",
"SOME_WHILE",
"SOME_WHILE_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(EVAL_FUN Skip s = SOME s)
/\
(EVAL_FUN (GenAssign v e) s = SOME(Update v e s))
/\
(EVAL_FUN (Dispose v) s = SOME(s \\ v))
/\
(EVAL_FUN (Seq c1 c2) s = EVAL_FUN c1 s >>= EVAL_FUN c2)
/\
(EVAL_FUN (Cond b c1 c2) s =
if beval b s then EVAL_FUN c1 s else EVAL_FUN c2 s)
/\
(EVAL_FUN (AnWh... | Define | EVAL_FUN_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN",
"IN",
"SOME_WHILE",
"Update"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
!c s1 s2.
EVAL c s1 s2
==>
(\c s1 s2. EVAL_FUN c s1 = SOME s2) c s1 s2 | IndDefRules.RULE_TAC
(IndDefRules.derive_mono_strong_induction [] (rules,induction))
THEN RW_TAC std_ss [EVAL_FUN_def,SOME_BIND_def]
THENL
[METIS_TAC[SOME_WHILE_REC,optionTheory.option_CLAUSES],
SIMP_TAC std_ss [Once SOME_WHILE_REC]
THEN RW_TAC std_ss [SOME_BIND_def]] | prove | EVAL_IMP_EVAL_FUN_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN",
"EVAL_FUN_def",
"SOME_BIND_def",
"SOME_WHILE_REC",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c s1.
(?s2. EVAL c s1 s2)
==>
!s2. EVAL c s1 s2 = (SOME s2 = EVAL_FUN c s1) | RW_TAC std_ss []
THEN IMP_RES_TAC EVAL_IMP_EVAL_FUN_LEMMA
THEN FULL_SIMP_TAC std_ss []
THEN METIS_TAC [EVAL_DETERMINISTIC] | store_thm | EVAL_EVAL_FUN | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_DETERMINISTIC",
"EVAL_FUN",
"EVAL_IMP_EVAL_FUN_LEMMA"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!f c. (!s1 s2. (f s1 = SOME s2) ==> EVAL c s1 s2)
==>
!n b s1 s2.
(IS_SOME(SOME_FUNPOW f n s1) /\ ~beval b (THE(SOME_FUNPOW f n s1)))
/\
(!m. IS_SOME(SOME_FUNPOW f m s1) /\ ~beval b (THE(SOME_FUNPOW f m s1)) ==> n <= m)
/\
(SOME_FUNPOW f ... | STRIP_TAC THEN STRIP_TAC THEN STRIP_TAC
THEN Induct
THEN RW_TAC (srw_ss()) [SOME_FUNPOW_def]
THENL
[METIS_TAC[rules],
Cases_on `f s1`
THEN FULL_SIMP_TAC (srw_ss()) []
THEN `!m. IS_SOME (SOME_FUNPOW f m s1) /\
~beval b (THE (SOME_FUNPOW f m s1)) ==>
... | store_thm | Least_AnWhile_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SOME_11",
"SOME_FUNPOW",
"SOME_FUNPOW_def",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!f c. (!s1 s2. (f s1 = SOME s2) ==> EVAL c s1 s2)
==>
!b s1 s2.
(?n. IS_SOME(SOME_FUNPOW f n s1) /\ ~beval b (THE(SOME_FUNPOW f n s1)))
/\
(SOME_FUNPOW f
(LEAST n. IS_SOME(SOME_FUNPOW f n s1) /\ ~beval b (THE(SOME_FUNPOW f n s1)))
s1 ... | REPEAT STRIP_TAC
THEN ASSUM_LIST
(fn thl=>
ASSUME_TAC
(SIMP_RULE (srw_ss()) thl
(Q.SPECL
[`LEAST n. IS_SOME(SOME_FUNPOW f n s1) /\ ~beval b (THE (SOME_FUNPOW f n s1))`,
`b`,`s1`,`s2`]
(MATCH_MP Least_AnWhile_LEMMA (el ... | store_thm | LEAST_AnWhile | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"FULL_LEAST_INTRO",
"Least_AnWhile_LEMMA",
"SOME_FUNPOW",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c s1 s2.
(EVAL_FUN c s1 = SOME s2)
==>
EVAL c s1 s2 | Induct
THEN RW_TAC std_ss
[EVAL_FUN_def,SOME_BIND_def,rules,
SKIP_THM,GEN_ASSIGN_THM,DISPOSE_THM,SEQ_THM,
IF_T_THM,IF_F_THM,ANWHILE_T_THM,
ANWHILE_F_THM,LOCAL_THM]
THEN FULL_SIMP_TAC (srw_ss()) []
THEN TRY(Cases_on `EVAL_FUN c s1`
THEN FULL_SIMP_TAC (... | prove | EVAL_FUN_IMP_EVAL_LEMMA | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ANWHILE_F_THM",
"ANWHILE_T_THM",
"DISPOSE_THM",
"EVAL_FUN",
"EVAL_FUN_def",
"GEN_ASSIGN_THM",
"IF_F_THM",
"IF_T_THM",
"LEAST_AnWhile",
"LOCAL_THM",
"SEQ_THM",
"SKIP_THM",
"SOME_BIND_def",
"SOME_WHILE_LEAST"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!c s1 s2. (EVAL_FUN c s1 = SOME s2) = EVAL c s1 s2 | METIS_TAC[EVAL_FUN_IMP_EVAL_LEMMA,EVAL_IMP_EVAL_FUN_LEMMA] | store_thm | EVAL_FUN_EVAL | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN",
"EVAL_FUN_IMP_EVAL_LEMMA",
"EVAL_IMP_EVAL_FUN_LEMMA"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(EVAL_FUN Skip s = SOME s)
/\
(EVAL_FUN (GenAssign v e) s = SOME(Update v e s))
/\
(EVAL_FUN (Dispose v) s = SOME(s \\ v))
/\
(EVAL_FUN (Seq c1 c2) s = EVAL_FUN c1 s >>= EVAL_FUN c2)
/\
(EVAL_FUN (Cond b c1 c2) s =
if beval b s then EVAL_FUN c1 s else EVAL_FUN c2 s)
/... | RW_TAC std_ss [EVAL_FUN_def,SOME_WHILE_REC]
THEN RW_TAC (srw_ss()) [SOME_BIND_def]
THEN Cases_on `EVAL_FUN c s`
THEN FULL_SIMP_TAC (srw_ss()) []
THEN METIS_TAC[EVAL_FUN_def] | store_thm | EVAL_FUN | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN_def",
"IN",
"SOME_BIND_def",
"SOME_WHILE_REC",
"Update"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
EVAL_CONT c cont s = EVAL_FUN c s >>= cont | Define | EVAL_CONT_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_CONT",
"EVAL_FUN"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
(!cont. EVAL_CONT Skip cont s = cont s)
/\
(!cont. EVAL_CONT (GenAssign v e) cont s = cont(Update v e s))
/\
(!cont. EVAL_CONT (Dispose v) cont s = cont(s \\ v))
/\
(!cont. EVAL_CONT (Seq c1 c2) cont s = EVAL_CONT c1 (EVAL_CONT c2 cont) s)
/\
(!cont. EVAL_CONT (Cond b c1 c2) cont... | RW_TAC std_ss [EVAL_CONT_def,EVAL_FUN_def,SOME_MONAD_LAWS]
THENL
[RW_TAC std_ss [SOME_BIND_def]
THEN Cases_on `EVAL_FUN c1 s`
THEN FULL_SIMP_TAC (srw_ss())[]
THEN Cases_on `EVAL_FUN c2 x`
THEN FULL_SIMP_TAC (srw_ss())[EVAL_CONT_def,SOME_MONAD_LAWS,SOME_BIND_def],
RW_TAC std_ss [SOME... | store_thm | EVAL_CONT | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_CONT_def",
"EVAL_FUN",
"EVAL_FUN_def",
"IN",
"SOME_BIND_def",
"SOME_MONAD_LAWS",
"SOME_WHILE",
"SOME_WHILE_NONE_CASES",
"SOME_WHILE_SOME_CASES",
"Update",
"option_CLAUSES"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SP P c = \s'. ?s. P s /\ (SOME s' = EVAL_FUN c s) | Define | SP_def | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN",
"SP"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | ||
SPEC P c (SP P c) /\ !Q. SPEC P c Q ==> !s. SP P c s ==> Q s | METIS_TAC[SPEC_def,SP_def,EVAL_FUN_EVAL] | store_thm | SP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN_EVAL",
"SPEC_def",
"SP_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SPEC P c Q = !s. SP P c s ==> Q s | METIS_TAC [SPEC_def,SP_def,EVAL_FUN_EVAL] | store_thm | SP_SPEC | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN_EVAL",
"SP",
"SPEC_def",
"SP_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
(!P c. RSPEC P c (\s1 s2. SP (\s. (s = s1) /\ P s1) c s2))
/\
(!P c R. RSPEC P c R = !s1 s2. SP (\s. (s = s1) /\ P s1) c s2 ==> R s1 s2) | RW_TAC std_ss [RSPEC_def,SP_def]
THEN METIS_TAC[EVAL_FUN_EVAL] | store_thm | RSPEC_SP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"EVAL_FUN_EVAL",
"RSPEC_def",
"SP",
"SP_def"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SP P Skip = P | CONV_TAC FUN_EQ_CONV
THEN CONV_TAC EVAL
THEN METIS_TAC[] | store_thm | SKIP_SP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SP"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!s0 P.
SP (\s. (s = s0) /\ P s0) Skip = \s'. (s' = s0) /\ P s0 | RW_TAC std_ss [SKIP_SP]
THEN METIS_TAC[] | store_thm | SKIP_SP_EX | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SKIP_SP",
"SP"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SP P (GenAssign v e) = \s'. ?s. P s /\ (s' = Update v e s) | CONV_TAC EVAL
THEN METIS_TAC[SUBSET_DEF] | store_thm | GEN_ASSIGN_SP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SP",
"SUBSET_DEF",
"Update"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!s0 P v e.
SP (\s. (s = s0) /\ P s0) (GenAssign v e) =
\s'. (s' = Update v e s0) /\ P s0 | RW_TAC std_ss [GEN_ASSIGN_SP]
THEN METIS_TAC[] | store_thm | GEN_ASSIGN_SP_EX | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"GEN_ASSIGN_SP",
"SP",
"Update"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!s0 P v e.
SP (\s. (s = s0) /\ P s0) (Assign v e) =
\s'. (s' = s0 |+ (v, Scalar (neval e s0))) /\ P s0 | RW_TAC std_ss [GEN_ASSIGN_SP,Assign_def,UpdateCases]
THEN METIS_TAC[] | store_thm | ASSIGN_SP_EX | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"Assign_def",
"GEN_ASSIGN_SP",
"SP",
"UpdateCases"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!s0 P v e1 e2.
SP (\s. (s = s0) /\ P s0) (ArrayAssign v e1 e2) =
\s'. (s' = s0 |+ (v, Array (aeval (ArrUpdate (ArrVar v) e1 e2) s0))) /\ P s0 | RW_TAC std_ss [GEN_ASSIGN_SP,ArrayAssign_def,UpdateCases]
THEN METIS_TAC[] | store_thm | ARRAY_ASSIGN_SP_EX | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"ArrayAssign_def",
"GEN_ASSIGN_SP",
"SP",
"UpdateCases"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
SP P (Dispose v) = \s'. ?s. P s /\ (s' = s \\ v) | CONV_TAC EVAL
THEN METIS_TAC[SUBSET_DEF] | store_thm | DISPOSE_SP | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"SP",
"SUBSET_DEF"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb | |
!s0 P v.
SP (\s. (s = s0) /\ P s0) (Dispose v) =
\s'. (s' = s0 \\ v) /\ P s0 | RW_TAC std_ss [DISPOSE_SP]
THEN METIS_TAC[] | store_thm | DISPOSE_SP_EX | examples.acl2.examples | examples/acl2/examples/fmapExample.sml | [] | [
"DISPOSE_SP",
"SP"
] | https://github.com/HOL-Theorem-Prover/HOL | ab6450c497d986a09043c9e930c36841ba93fbdb |
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